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arXiv · 1103.4230

Stable pairs on local K3 surfaces

Yukinobu Toda
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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 multi-covering 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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BibTeXRIS

Yukinobu Toda. 2012-06-27. Stable pairs on local K3 surfaces. https://arxiv.org/abs/1103.4230

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