Vafa-Witten invariants for projective surfaces II: semistable case
Algebraic Geometry
2022-10-11 v4 High Energy Physics - Theory
Differential Geometry
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 we expect our definition coincides with an alternative definition using weighted Euler characteristics. We prove this for deg here, and it is proved for a K3 surface in \cite{MT}. For K3 surfaces we calculate the invariants in terms of modular forms which generalise and prove conjectures of Vafa and Witten.
Cite
@article{arxiv.1702.08488,
title = {Vafa-Witten invariants for projective surfaces II: semistable case},
author = {Yuuji Tanaka and Richard P. Thomas},
journal= {arXiv preprint arXiv:1702.08488},
year = {2022}
}
Comments
Error found by Laarakker fixed. To appear in Pure Appl. Math. Quart. (2017), issue in honour of 60th birthday of Simon Donaldson. 37 pages