Vafa-Witten invariants for projective surfaces II: semistable case

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Title: Vafa-Witten invariants for projective surfaces II: semistable case
Authors: Tanaka, Y
Thomas, RP
Item Type: Journal Article
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.
Issue Date: 12-Nov-2018
Date of Acceptance: 12-Nov-2018
URI: http://hdl.handle.net/10044/1/65189
DOI: https://dx.doi.org/10.4310/PAMQ.2017.v13.n3.a6
ISSN: 1558-8599
Publisher: International Press
Start Page: 517
End Page: 562
Journal / Book Title: Pure and Applied Mathematics Quarterly
Volume: 13
Issue: 3
Copyright Statement: © 2018 by International Press of Boston, Inc. All rights reserved.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/R013349/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
DONALDSON-THOMAS INVARIANTS
ARTIN STACKS
ABELIAN CATEGORIES
YANG-MILLS
CONFIGURATIONS
STRINGS
SHEAVES
MODULI
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
DONALDSON-THOMAS INVARIANTS
ARTIN STACKS
ABELIAN CATEGORIES
YANG-MILLS
CONFIGURATIONS
STRINGS
SHEAVES
MODULI
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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