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October 2012 Stable pairs on local $K3$ surfaces
Yukinobu Toda
J. Differential Geom. 92(2): 285-370 (October 2012). DOI: 10.4310/jdg/1352297809

Abstract

We prove a formula which relates Euler characteristic of moduli spaces of stable pairs on local $K3$ surfaces to counting invariants of semistable sheaves on them. Our formula generalizes Kawai- Yoshioka’s formula for stable pairs with irreducible curve classes to arbitrary curve classes. We also propose a conjectural multiple cover formula of sheaf counting invariants which, combined with our main result, leads to an Euler characteristic version of Katz- Klemm-Vafa conjecture for stable pairs.

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Yukinobu Toda. "Stable pairs on local $K3$ surfaces." J. Differential Geom. 92 (2) 285 - 370, October 2012. https://doi.org/10.4310/jdg/1352297809

Information

Published: October 2012
First available in Project Euclid: 7 November 2012

zbMATH: 1260.14045
MathSciNet: MR2998674
Digital Object Identifier: 10.4310/jdg/1352297809

Rights: Copyright © 2012 Lehigh University

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Vol.92 • No. 2 • October 2012
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