Invariants of moduli spaces of stable sheaves on ruled surfaces

Abstract

We compute Betti numbers of the moduli spaces of arbitrary rank stable sheaves on ruled surfaces. Our result generalizes the formula of Goettsche for rank one sheaves and the formula of Yoshioka for rank two sheaves. It also confirms the conjecture of Manschot for arbitrary rank sheaves on the Hirzebruch surfaces.

arXiv comment26 pages

References in corpus (7)

• 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
• Mixed Hodge structures of configuration spaces
• A computational criterion for the Kac conjecture
• Motivic Donaldson-Thomas invariants and McKay correspondence
• Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces
• Wall-crossing formulas for framed objects

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• S-duality and refined BPS indices
• Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces
• From strings in 6d to strings in 5d
• Vafa-Witten invariants from modular anomaly
• Intersection cohomology of moduli spaces of sheaves on surfaces
• Twisted sheaves and $\mathrm{SU}(r)/{\mathbb{Z}}_r$ Vafa-Witten theory
• Sheaves on surfaces and virtual invariants
• Generalized Donaldson-Thomas invariants on the local projective plane
• On the stabilization of the Betti numbers of the moduli space of sheaves on ${\mathbb{P}}^2$
• Motivic measures of the moduli spaces of pure sheaves on ${\mathbb{P}}^2$ with all degrees