Vafa-Witten invariants for projective surfaces II: semistable case

Author: 

Thomas, R
Tanaka, Y

Publication Date: 

1 January 2018

Journal: 

Pure and Applied Mathematics Quarterly

Last Updated: 

2020-04-02T07:34:23.193+01:00

Issue: 

3

Volume: 

13

DOI: 

10.4310/PAMQ.2017.v13.n3.a6

page: 

517–562-

abstract: 

<p>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.</p> <br/> <p>For KS ≤ 0 we expect our definition coincides with an alternative definition using weighted Euler characteristics. We prove this for degKS &lt; 0 here, and it is proved for S a K3 surface in [MT].</p> <br/> <p>For K3 surfaces we calculate the invariants in terms of modular forms which generalise and prove conjectures of Vafa and Witten.</p>

Symplectic id: 

871236

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article