Stable pairs on local K3 surfaces
Yukinobu Toda
TL;DR
This paper establishes a formula connecting the Euler characteristics of moduli spaces of stable pairs on local K3 surfaces with sheaf counting invariants, extending previous results and proposing a conjecture related to the Katz-Klemm-Vafa conjecture.
Contribution
It generalizes Kawai-Yoshioka's stable pairs formula to all curve classes and introduces a conjectural multi-covering formula for sheaf invariants.
Findings
Derived a formula relating Euler characteristics to sheaf invariants.
Extended stable pairs formula to arbitrary curve classes.
Proposed a conjecture linking to Katz-Klemm-Vafa conjecture.
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds