Paper Citation Record · LEDGER

Hassett--Keel Program in genus four

As of 22 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 2 inbound Pith citation observations for arXiv:2504.20312.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2504.20312 v1

Coverage vector

measured 60 of 60 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-16T05:46:44.255260Z

measured 62 of 62 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T14:55:04.236786Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-19T03:52:01.463854Z

Reference resolution

60 of 60 outbound references displayed

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Outbound references

Observation a8fea70c-7044-4892-afc1-cc8aaa04a22a · outbound

This paper cites Moduli of boundary polarized Calabi-Yau pairs.

Hassett--Keel Program in genus four Moduli of boundary polarized Calabi-Yau pairs

Reference 1

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Observation 25e39db7-be7c-4ece-a332-0f34f398b68f · outbound

This paper cites Reductivity of the automorphism group of K -polystable F ano varieties.

Hassett--Keel Program in genus four Reductivity of the automorphism group of K -polystable F ano varieties

Reference 2

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Observation d434f520-72a9-4a33-a408-2189f95a706c · outbound

This paper cites Wall crossing for moduli of stable log pairs.

Hassett--Keel Program in genus four Wall crossing for moduli of stable log pairs

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.515228Z

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Observation a744ee73-8ce5-481b-9977-04734ebbd77f · outbound

This paper cites Mirror symmetry and the classification of orbifold del P ezzo surfaces.

Hassett--Keel Program in genus four Mirror symmetry and the classification of orbifold del P ezzo surfaces

Reference 4

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Observation c4893887-7b26-4119-8372-bce25e10b6c8 · outbound

This paper cites Geometry of algebraic curves: volume II with a contribution by Joseph Daniel Harris.

Hassett--Keel Program in genus four Geometry of algebraic curves: volume II with a contribution by Joseph Daniel Harris

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.468176Z

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Observation 405bbb16-304e-4e8d-aa9e-576ca123e4ae · outbound

This paper cites K-moduli of curves on a quadric surface and K 3 surfaces.

Hassett--Keel Program in genus four K-moduli of curves on a quadric surface and K 3 surfaces

Reference 6

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Observation d56d8236-d766-4740-b59b-0807b6b342d4 · outbound

This paper cites Wall crossing for K -moduli spaces of plane curves.

Hassett--Keel Program in genus four Wall crossing for K -moduli spaces of plane curves

Reference 7

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Observation 06832c6c-d7d6-4d0a-9ff1-f0b2f7a70224 · outbound

This paper cites Singularities with G _m -action and the log minimal model program for M _g.

Hassett--Keel Program in genus four Singularities with G _m -action and the log minimal model program for M _g

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.415642Z

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Observation 8c0694c9-1679-4347-8cba-44ce61e3364c · outbound

This paper cites Second flip in the H assett- K eel program: existence of good moduli spaces.

Hassett--Keel Program in genus four Second flip in the H assett- K eel program: existence of good moduli spaces

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.392923Z

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Observation 3c58f465-6744-45c1-a066-76d494f9d98f · outbound

This paper cites Second flip in the H assett- K eel program: projectivity.

Hassett--Keel Program in genus four Second flip in the H assett- K eel program: projectivity

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.366480Z

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Observation ebab56db-d21e-49a9-8a4f-bf50e7c3ae81 · outbound

This paper cites Second flip in the H assett- K eel program: a local description.

Hassett--Keel Program in genus four Second flip in the H assett- K eel program: a local description

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.341117Z

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Observation 7d3bed80-9c26-4e4f-97cc-af46a405ce18 · outbound

This paper cites Existence of moduli spaces for algebraic stacks.

Hassett--Keel Program in genus four Existence of moduli spaces for algebraic stacks

Reference 12

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Observation d2b237a5-6fa8-4cc2-839a-f6a217dd70c2 · outbound

This paper cites A L una \' e tale slice theorem for algebraic stacks.

Hassett--Keel Program in genus four A L una \' e tale slice theorem for algebraic stacks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.294368Z

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Observation c1eb477f-fbfe-4a83-a8eb-eb1781a321cf · outbound

This paper cites Good moduli spaces for A rtin stacks.

Hassett--Keel Program in genus four Good moduli spaces for A rtin stacks

Reference 14

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Observation 0f06123d-6a7f-429e-915d-8504cc68434c · outbound

This paper cites Stacks of cyclic covers of projective spaces.

Hassett--Keel Program in genus four Stacks of cyclic covers of projective spaces

Reference 15

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Observation ac40274a-0d1f-41c3-b93f-2889e67cf3a1 · outbound

This paper cites Hacon, and James McKernan.

Hassett--Keel Program in genus four Hacon, and James McKernan

Reference 16

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Observation 84b68e91-f11b-4ab0-80d3-adcb40903358 · outbound

This paper cites Ribbons and their canonical embeddings.

Hassett--Keel Program in genus four Ribbons and their canonical embeddings

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.232926Z

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Observation fe7ab25f-7a17-4c58-ad0f-5dad0f7922c9 · outbound

This paper cites Good moduli spaces for boundary polarized Calabi-Yau surface pairs.

Hassett--Keel Program in genus four Good moduli spaces for boundary polarized Calabi-Yau surface pairs

Reference 18

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Observation fb3a611b-2f67-4295-801d-2aa256fa4ea1 · outbound

This paper cites On C how stability for algebraic curves.

Hassett--Keel Program in genus four On C how stability for algebraic curves

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.211601Z

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Observation e0b31f1b-13f2-41c9-82ea-89a35711267f · outbound

This paper cites Nagata compactification for algebraic spaces.

Hassett--Keel Program in genus four Nagata compactification for algebraic spaces

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.190497Z

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Observation 187b2b0e-b157-41dd-a695-c9f19c46540e · outbound

This paper cites The geometry of the ball quotient model of the moduli space of genus four curves.

Hassett--Keel Program in genus four The geometry of the ball quotient model of the moduli space of genus four curves

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.168069Z

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Observation 8851e2ee-5833-4036-9766-eecab0cb6396 · outbound

This paper cites Log canonical models and variation of GIT for genus 4 canonical curves.

Hassett--Keel Program in genus four Log canonical models and variation of GIT for genus 4 canonical curves

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.143970Z

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Observation 2e411e7e-48d3-47bc-90c3-181101f99656 · outbound

This paper cites Dolgachev and Yi Hu.

Hassett--Keel Program in genus four Dolgachev and Yi Hu

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.123123Z

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Observation 2eed9404-242d-4324-84e9-d120f2158fc7 · outbound

This paper cites Stable log surfaces, admissible covers, and canonical curves of genus 4.

Hassett--Keel Program in genus four Stable log surfaces, admissible covers, and canonical curves of genus 4

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.102057Z

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Observation 112cce6d-1e7e-4c11-9b84-1a839c088a09 · outbound

This paper cites an unresolved cited work.

Hassett--Keel Program in genus four Unresolved cited work

Reference 25

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Observation 7fa25a7f-5f5c-4a93-9638-97de57dfade3 · outbound

This paper cites Deligne and D.

Hassett--Keel Program in genus four Deligne and D

Reference 26

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Observation adac4a14-879d-4676-aecc-064916eaed28 · outbound

This paper cites The final log canonical model of the moduli space of stable curves of genus 4.

Hassett--Keel Program in genus four The final log canonical model of the moduli space of stable curves of genus 4

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.038330Z

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Observation 3aa4c9fc-27d5-4ae9-8702-13023c2761f7 · outbound

This paper cites Compact moduli of plane curves.

Hassett--Keel Program in genus four Compact moduli of plane curves

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:45.016184Z

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Observation 1ee31de2-8802-419f-b448-18ca866a9384 · outbound

This paper cites Algebraic geometry.

Hassett--Keel Program in genus four Algebraic geometry

Reference 29

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Observation cf0a27d1-22e8-4b4b-a3b1-b60f2629a422 · outbound

This paper cites Classical and minimal models of the moduli space of curves of genus two.

Hassett--Keel Program in genus four Classical and minimal models of the moduli space of curves of genus two

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.981366Z

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Observation 2dbf600f-93b2-4163-b66b-6a1875e939e3 · outbound

This paper cites Log canonical models for the moduli space of curves: the first divisorial contraction.

Hassett--Keel Program in genus four Log canonical models for the moduli space of curves: the first divisorial contraction

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.961448Z

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Observation e8eaf117-f788-430f-a25e-d4080cc32329 · outbound

This paper cites Log minimal model program for the moduli space of stable curves: the first flip.

Hassett--Keel Program in genus four Log minimal model program for the moduli space of stable curves: the first flip

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.943244Z

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Observation d90ba899-069c-4bcd-806b-c00506f8cb86 · outbound

This paper cites Stability of tri-canonical curves of genus two.

Hassett--Keel Program in genus four Stability of tri-canonical curves of genus two

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.925636Z

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Observation 299e3861-bfac-4037-b946-92c52d338e2c · outbound

This paper cites Log minimal model program for the moduli space of stable curves of genus three.

Hassett--Keel Program in genus four Log minimal model program for the moduli space of stable curves of genus three

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.902180Z

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Observation fd6873fb-1c10-426e-b4fe-ea32ddda469e · outbound

This paper cites A birational contraction of genus 2 tails in the moduli space of genus 4 curves I.

Hassett--Keel Program in genus four A birational contraction of genus 2 tails in the moduli space of genus 4 curves I

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.877078Z

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Observation 315cc7c5-fd30-4cd2-8990-931aec44957b · outbound

This paper cites Projectivity of the moduli of equidimensional branchvarieties.

Hassett--Keel Program in genus four Projectivity of the moduli of equidimensional branchvarieties

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-16T05:46:44.402706Z

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Observation affe9919-4c0e-4b87-8d38-d49267d192d7 · outbound

This paper cites Moduli of curves , volume 187 of Graduate Texts in Mathematics.

Hassett--Keel Program in genus four Moduli of curves , volume 187 of Graduate Texts in Mathematics

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.858271Z

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Observation 9f503c11-97e3-4c54-954a-524030968f6a · outbound

This paper cites Smoothable del P ezzo surfaces with quotient singularities.

Hassett--Keel Program in genus four Smoothable del P ezzo surfaces with quotient singularities

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.839231Z

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Observation ef31ab23-2f25-44cd-be50-7fc643122d5b · outbound

This paper cites an unresolved cited work.

Hassett--Keel Program in genus four Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-16T05:46:44.818373Z

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Observation a21530ab-d2f9-456b-8364-fc39c172d8d8 · outbound

This paper cites Classification of three-dimensional flips.

Hassett--Keel Program in genus four Classification of three-dimensional flips

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.794940Z

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Observation 4c5a845d-fb9f-4863-8112-36858a0f4e27 · outbound

This paper cites Birational geometry of algebraic varieties , volume 134 of Cambridge Tracts in Mathematics.

Hassett--Keel Program in genus four Birational geometry of algebraic varieties , volume 134 of Cambridge Tracts in Mathematics

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:43.974234Z

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Observation bb218789-ddcf-4c6a-9584-aeb438035abf · outbound

This paper cites Rational curves on algebraic varieties , volume 32 of Ergebnisse der Mathematik und ihrer Grenzgebiete.

Hassett--Keel Program in genus four Rational curves on algebraic varieties , volume 32 of Ergebnisse der Mathematik und ihrer Grenzgebiete

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:43.979983Z

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Observation b0dcf5c6-5679-444d-8e39-0fa4744663d1 · outbound

This paper cites Families of varieties of general type , volume 231 of Cambridge Tracts in Mathematics.

Hassett--Keel Program in genus four Families of varieties of general type , volume 231 of Cambridge Tracts in Mathematics

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.743760Z

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Observation ba4a4f8a-ca83-468b-bd3d-4ac902ca8a5f · outbound

This paper cites The moduli space of curves of genus 4 and Deligne - Mostow 's complex reflection groups.

Hassett--Keel Program in genus four The moduli space of curves of genus 4 and Deligne - Mostow 's complex reflection groups

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.719455Z

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Observation 1463e404-6ba4-43dd-9c9f-182d7693faf8 · outbound

This paper cites Positivity in algebraic geometry.

Hassett--Keel Program in genus four Positivity in algebraic geometry

Reference 45

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Observation 724a1699-27da-48f4-8c2a-dd040adb90a8 · outbound

This paper cites G IT versus B aily- B orel compactification for K3 's which are double covers of P^1 P^1.

Hassett--Keel Program in genus four G IT versus B aily- B orel compactification for K3 's which are double covers of P^1 P^1

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.680389Z

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Observation 441bbe75-3103-4113-9a86-e12c9a3a5bdc · outbound

This paper cites K-moduli of Fano threefolds and genus four curves.

Hassett--Keel Program in genus four K-moduli of Fano threefolds and genus four curves

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.149528Z

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Observation 3ddd0b09-9f6e-4a1a-a2bf-559791af3a38 · outbound

This paper cites Mori theory of moduli spaces of stable curves.

Hassett--Keel Program in genus four Mori theory of moduli spaces of stable curves

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.655874Z

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Observation 327cc57f-8c3c-4695-bc02-aa1783defe22 · outbound

This paper cites Stability of projective varieties , volume No.

Hassett--Keel Program in genus four Stability of projective varieties , volume No

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.633380Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f3b812b4-353f-4582-87cf-5810cea459d8 · outbound

This paper cites MMP for locally stable families and wall crossing for moduli of stable pairs.

Hassett--Keel Program in genus four MMP for locally stable families and wall crossing for moduli of stable pairs

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.168098Z

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Observation 1a95f6f2-180c-4a03-9c3f-baed3a81fd89 · outbound

This paper cites Le th\' e or\` e me de compactification de Nagata pour les espaces alg\' e briques.

Hassett--Keel Program in genus four Le th\' e or\` e me de compactification de Nagata pour les espaces alg\' e briques

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.612465Z

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Observation cb75b95e-fbef-4ce2-a1f5-e7bb2fad6727 · outbound

This paper cites A new compactification of the moduli space of curves.

Hassett--Keel Program in genus four A new compactification of the moduli space of curves

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.179470Z

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Unavailable: canonical work link unavailable.

Observation dc6d3584-f253-419e-b1b9-6939fd54a763 · outbound

This paper cites Deformations of algebraic schemes , volume 334 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences].

Hassett--Keel Program in genus four Deformations of algebraic schemes , volume 334 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.185335Z

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Unavailable: canonical work link unavailable.

Observation 20a07888-6207-44c0-b5a2-054eb5ac39e1 · outbound

This paper cites Towards a classification of modular compactifications of M _ g,n.

Hassett--Keel Program in genus four Towards a classification of modular compactifications of M _ g,n

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.552841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a7fef9a5-3f5f-4ac5-a343-84bf43b739b3 · outbound

This paper cites Stacks Project.

Hassett--Keel Program in genus four Stacks Project

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.218260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00862088-c4ce-4826-b541-34d9ce72415c · outbound

This paper cites Geometric invariant theory and flips.

Hassett--Keel Program in genus four Geometric invariant theory and flips

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.227306Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99d0dce5-3da5-4ab5-88b7-834a5ef4e4d6 · outbound

This paper cites K-stability of F ano varieties , volume 50 of New Mathematical Monographs.

Hassett--Keel Program in genus four K-stability of F ano varieties , volume 50 of New Mathematical Monographs

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T05:46:44.507346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e95503f6-3762-4717-99c8-b7174055a872 · outbound

This paper cites The Moduli Space of Genus Six Curves and K-stability: VGIT and the Hassett-Keel Program.

Hassett--Keel Program in genus four The Moduli Space of Genus Six Curves and K-stability: VGIT and the Hassett-Keel Program

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.242033Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53554558-33bc-404b-b502-523b3851a5d9 · outbound

This paper cites Moduli of genus six curves and K -stability.

Hassett--Keel Program in genus four Moduli of genus six curves and K -stability

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.248780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8de11497-05cc-427b-a8ce-2d3e0a87aaac · outbound

This paper cites On wall-crossing for K -stability.

Hassett--Keel Program in genus four On wall-crossing for K -stability

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-16T05:46:44.255260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 62ae2e11-2efc-4245-884b-0db2e86e21b8 · inbound

Remarks on two problems by Hassett cites this paper.

Remarks on two problems by Hassett Hassett--Keel Program in genus four

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-19T03:52:01.465683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c142957d-01b4-4bc2-9f72-5fb8e211b4ba · inbound

Normal stable degenerations of Noether-Horikawa surfaces cites this paper.

Normal stable degenerations of Noether-Horikawa surfaces Hassett--Keel Program in genus four

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T14:55:04.236786Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.