Stable pairs on local K3 surfaces

2011/03/22 by Yukinobu Toda, Toda, Yukinobu
Mathematics · #14N35 #18E30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1103.4230

openalex publication_date 2011/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Gromov-Witten theory and Noether-Lefschetz theory
• Donaldson-Thomas invariants via microlocal geometry
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

Related

• Stable pairs on elliptic K3 surfaces
• Moduli of stable sheaves supported on curves of genus three contained in a quadric surface
• Refined sheaf counting on local K3 surfaces
• Stable pairs on curves and surfaces
• Moduli of sheaves supported on curves of genus two in a quadric surface