English

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