Hodge numbers of moduli spaces of stable bundles on K3 surfaces

1994/08/04 by Goettsche, Lothar, Daniel Huybrechts, Huybrechts, Daniel · 1 citation
Mathematics · #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.alg-geom/9408001

openalex publication_date 1994/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Hodge numbers of the moduli space of stable rank two sheaves with primitive determinant on a K3 surface coincide with the Hodge numbers of an appropriate Hilbert scheme of points on the K3 surface. The precise result is: Theorem: Let X be a K3 surface, L a primitive big and nef line bundle and H a generic polarization. If the moduli space of rank two H semi-stable torsion-free sheaves with determiant L and second Chern class c₂ has at least dimension 10 then its Hodge numbers coincide with those of the Hilbert scheme of l:=2c₂-(L²)/(2)-3 points on X.

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• Some notes on the moduli of stable sheaves on elliptic surfaces

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