Pith. sign in

REVIEW 3 cited by

The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces

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 2205.12953 v2 pith:WLDB7GSP submitted 2022-05-25 math.AG

The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces

Nikolas Kuhn , Oliver Leigh , Yuuji Tanaka This is my paper
classification math.AG
keywords formulasheavessurfacessettingblow-upframedgeneragieseker
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

We prove a blow-up formula for the generating series of virtual $\chi_y$-genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topological $\chi_y$-genera of G\"ottsche. Our formula is a refinement of one by Vafa-Witten relating to S-duality. We prove the formula simultaneously in the setting of Gieseker stable sheaves on polarised surfaces and also in the setting of framed sheaves on $\mathbb{P}^2$. The proof is based on the blow-up algorithm of Nakajima-Yoshioka for framed sheaves on $\mathbb{P}^2$, which has recently been extend to the setting of Gieseker $H$-stable sheaves on $H$-polarised surfaces by Kuhn-Tanaka.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

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

  1. Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures

    math.AG 2026-06 unverdicted novelty 7.0

    Establishes Lagrangian correspondences and 2(1-dim X)-shifted pretwistor structures on derived moduli stacks of perfect complexes with connections, compatible with Riemann-Hilbert and PTVV symplectic geometry.

  2. Refined Vafa-Witten invariants for toric surfaces from supersymmetric localization in 5D gauge theory

    hep-th 2026-07 conditional novelty 6.0

    5D N=1* supersymmetric localization on toric surfaces equals refined Vafa–Witten invariants for odd first Chern class; the even-c1 case fails without a hand-added constant.

  3. Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures

    math.AG 2026-06 unverdicted novelty 5.0

    Proves Lagrangian correspondences in nonabelian Hodge theory for perfect complexes and establishes canonical shifted pretwistor structures on the Deligne-Hitchin-Simpson moduli stack over P^1_C.