The Tanaka-Thomas's Vafa-Witten invariants via surface Deligne-Mumford stacks
Algebraic Geometry
2021-10-05 v2
Abstract
We provide a definition of Vafa-Witten invariants for projective surface Deligne-Mumford stacks, generalizing the construction of Tanaka-Thomas on the Vafa-Witten invariants for projective surfaces inspired by the S-duality conjecture. We give calculations for a root stack over a general type quintic surface, and quintic surfaces with ADE singularities. The relationship between the Vafa-Witten invariants of quintic surfaces with ADE singularities and the Vafa-Witten invariants of their crepant resolutions is also discussed.
Keywords
Cite
@article{arxiv.1903.11477,
title = {The Tanaka-Thomas's Vafa-Witten invariants via surface Deligne-Mumford stacks},
author = {Yunfeng Jiang and Promit Kundu},
journal= {arXiv preprint arXiv:1903.11477},
year = {2021}
}
Comments
42 pages, comments are very welcome. revised according to the referee, Proposition 4.6 in the old version is corrected. Published version