Journal title
Journal of Algebraic Geometry
DOI
10.1090/jag/738
Last updated
2020-08-21T03:57:40.193+01:00
Page
1-1
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 $ \mathbb{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.
Symplectic ID
945778
Submitted to ORA
On
Publication type
Journal Article
Publication date
23 October 2019