On blowup formulae for the S-duality conjecture of Vafa and Witten

Abstract

This is the first part of two papers. In this part, we prove the blowup formulae for virtual Hodge polynomials of Gieseker moduli spaces of rank-2 stable sheaves and Uhlenbeck compactification spaces over algebraic surfaces. In particular, we verify the blowup formulae for the S-duality conjecture of Vafa-Witten, i.e. the blowup formulae for the Euler numbers of instanton moduli spaces over algebraic surfaces.

24 pages

Cited by in corpus (29)

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• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
• Theta functions and Hodge numbers of moduli spaces of sheaves on rational surfaces
• Vafa-Witten invariants from exceptional collections
• Virtual refinements of the Vafa-Witten formula
• A rank 2 Dijkgraaf-Moore-Verlinde-Verlinde formula
• Lectures on Instanton Counting
• Quantum geometry of elliptic Calabi-Yau manifolds
• Vafa-Witten invariants from modular anomaly
• Rank $N$ Vafa-Witten invariants, modularity and blow-up
• $O(-2)$ Blow-up Formula via Instanton Calculus on $\widehat{C^2/Z_2}$ and Weil Conjecture
• {\cal N}=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\mathbf{Z}}_2$: Higher Rank Case
• N=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\mathbf{Z}}_2$
• $S$-duality in Vafa-Witten theory for non-simply laced gauge groups
• Twisted sheaves and $\mathrm{SU}(r)/{\mathbb{Z}}_r$ Vafa-Witten theory
• Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes
• Flops and the S-duality conjecture
• Virtual ${\chi }_{-y}$-genera of Quot schemes on surfaces
• Donaldson-Thomas invariants of certain Calabi-Yau 3-folds
• Sheaves on surfaces and virtual invariants
• BPS invariants of semi-stable sheaves on rational surfaces
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Identities for generalized Appell functions and the blow-up formula
• Mock modularity at work, or black holes in a forest
• $\mathrm{SU}(r)$ Vafa-Witten invariants, Ramanujan's continued fractions, and cosmic strings
• Generalized Donaldson-Thomas invariants on the local projective plane
• A blowup formula for virtual enumerative invariants on projective surfaces
• The Vafa-Witten invariants via surface Deligne-Mumford stacks and S-duality
• On the motive of the Hilbert scheme of points on a surface