Pure and Applied Mathematics Quarterly
Volume 17 (2021)
The Tanaka–Thomas’s Vafa–Witten invariants via surface Deligne–Mumford stacks
Pages: 503 – 573
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.
The first author would like to thank Hong Kong University of Science and Technology for hospitality where part of the work is done. This work is partially supported by NSF DMS-1600997.
Received 25 February 2020
Accepted 29 December 2020
Published 11 April 2021