Pith. sign in

REVIEW 5 cited by

Local Mirror Symmetry at Higher Genus

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv hep-th/9906046 v3 pith:2ZIHAHCG submitted 1999-06-04 hep-th math.AG

Albrecht Klemm , Eric Zaslow This is my paper · ORCID
classification hep-thmath.AG
keywords localfunctionmirrorpartitioncurvesgopakumarhigher-genussymmetry
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We discuss local mirror symmetry for higher-genus curves. Specifically, we consider the topological string partition function of higher-genus curves contained in a Fano surface within a Calabi-Yau. Our main example is the local P^2 case. The Kodaira-Spencer theory of gravity, tailored to this local geometry, can be solved to compute this partition function. Then, using the results of Gopakumar and Vafa and the local mirror map, the partition function can be rewritten in terms of expansion coefficients, which are found to be integers. We verify, through localization calculations in the A-model, many of these Gromov-Witten predictions. The integrality is a mystery, mathematically speaking. The asymptotic growth (with degree) of the invariants is analyzed. Some suggestions are made towards an enumerative interpretation, following the BPS-state description of Gopakumar and Vafa.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Flux Vacua Near the Boundary of Large Complex Structure

    hep-th 2026-07 conditional novelty 6.0 of 10

    Near the boundary of large complex structure, the first worldsheet instanton can displace flux vacua significantly while higher instantons stay negligible, and such vacua are common in a bounded two-modulus scan.

  2. Large Order Enumerative Geometry, Black Holes and Black Rings

    hep-th 2026-05 unverdicted novelty 6.0 of 10

    Numerical study of high-genus GV invariants reveals 5D indices matching BMPV black-hole entropy below a critical angular momentum and black-ring dominance above, with additional phase transitions and growth laws in PT...

  3. Deep observations of the Type IIB flux landscape

    hep-th 2025-01 conditional novelty 6.0 of 10

    An enumeration algorithm for Type IIB flux vacua yields millions of explicit vacua in a two-modulus Calabi-Yau, exposing deviations from statistical predictions and a vacuum with |W0| about 5.5 x 10^-5.

  4. Non-Perturbative Real Topological Strings

    hep-th 2023-09 unverdicted novelty 6.0 of 10

    Extends operator formalism of closed topological strings to derive all-order trans-series solutions for real topological strings, with disk invariants as Stokes constants and numerical checks on local P2.

  5. Modular resurgence of topological string

    hep-th 2026-07 unverdicted novelty 5.0 of 10

    Stokes constants of topological string non-perturbative contributions are invariant on monodromy orbits, reproduce the BPS spectrum, and satisfy the Kontsevich-Soibelman Lie algebra.

Pith tools