Vafa-Witten invariants for projective surfaces I: stable case

File Description SizeFormat 
1702.08487v4.pdfFile embargoed until 01 January 10000648.08 kBAdobe PDF
Title: Vafa-Witten invariants for projective surfaces I: stable case
Authors: Tanaka, Y
Thomas, RP
Item Type: Journal Article
Abstract: On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a ℂ∗ action with compact fixed locus. Applying virtual localisation we define invariants constant under deformations. When the vanishing theorem of Vafa-Witten holds, the result is the (signed) Euler characteristic of the moduli space of instantons. In general there are other, rational, contributions. Calculations of these on surfaces with positive canonical bundle recover the first terms of modular forms predicted by Vafa and Witten.
Date of Acceptance: 22-Nov-2018
URI: http://hdl.handle.net/10044/1/64607
ISSN: 1534-7486
Publisher: American Mathematical Society
Start Page: 562
End Page: 562
Journal / Book Title: Journal of Algebraic Geometry
Copyright Statement: This paper is embargoed until publication. This paper is under copyright.
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
math.AG
math.AG
hep-th
math.DG
14N35, 14D20, 14D21, 14J60
math.AG
math.AG
hep-th
math.DG
14N35, 14D20, 14D21, 14J60
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Notes: Typo fixed. 61 pages
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commonsx