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arXiv · 2007.12730

Sheaves on surfaces and virtual invariants

L. Göttsche·M. Kool
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Abstract

Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection numbers, such as virtual Euler characteristics, Verlinde numbers, and Segre numbers. We survey a set of recent conjectures by the authors for these numbers with applications to Vafa-Witten theory, $K$-theoretic S-duality, a rank 2 Dijkgraaf-Moore-Verlinde-Verlinde formula, and a virtual Segre-Verlinde correspondence. A key role is played by Mochizuki's formula for descendent Donaldson invariants.

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BibTeXRIS

L. Göttsche, M. Kool. 2020-07-24. Sheaves on surfaces and virtual invariants. https://doi.org/10.4310/sdg.2019.v24.n1.a3

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