The Tanaka-Thomas's Vafa-Witten invariants via surface Deligne-Mumford stacks
arXiv:1903.11477
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.
arXiv comment42 pages, comments are very welcome. revised according to the referee, Proposition 4.6 in the old version is corrected. Published version
References in corpus (13)
- The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
- Donaldson-Thomas invariants via microlocal geometry
- Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds
- Vafa-Witten invariants for projective surfaces I: stable case
- Vafa-Witten invariants for projective surfaces II: semistable case
- Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks
- Virtual signed Euler characteristics
- Fixed point loci of moduli spaces of sheaves on toric varieties
- Monopole contributions to refined Vafa-Witten invariants
- Degeneracy loci, virtual cycles and nested Hilbert schemes I
- Mirror Symmetry on Kummer Type K3 Surfaces
- Shifted Symplectic Structures
- A boundary divisor in the moduli space of stable quintic surfaces