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Vafa-Witten invariants for projective surfaces II: semistable case

Authors
  • Tanaka, Y
  • Thomas, RP
Publication Date
Nov 12, 2018
Identifiers
DOI: 10.4310/PAMQ.2017.v13.n3.a6
OAI: oai:spiral.imperial.ac.uk:10044/1/65189
Source
Spiral - Imperial College Digital Repository
Keywords
License
Unknown

Abstract

We propose a definition of Vafa–Witten invariants counting semistable Higgs pairs on a polarised surface. We use virtual localisation applied to Mochizuki/Joyce–Song pairs. For KS≤0 we expect our definition coincides with an alternative definition using weighted Euler characteristics. We prove this for degKS<0 here, and it is proved for S a K3 surface in “Sheaf counting on local K3 surfaces” [D. Maulik and R. P. Thomas, arXiv:1806.02657]. For K3 surfaces we calculate the invariants in terms of modular forms which generalise and prove conjectures of Vafa and Witten.

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