Stability conditions and μ-stable sheaves on K3 surfaces with Picard number one

2010/05/21 by Kotaro Kawatani, Kawatani, Kotaro
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · doi:10.48550/arxiv.1005.3877

openalex publication_date 2010/05/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this article, we show that some semi-rigid μ-stable sheaves on a projective K3 surface X with Picard number 1 are stable in the sense of Bridgeland's stability condition. As a consequence of our work, we show that the special set U(X) ⊂ \Stab (X) reconstructs X itself. This gives a sharp contrast to the case of an abelian surface.

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• Stable Sheaves on K3 Surfaces via Wall-Crossing
• The cohomology of the general stable sheaf on a K3 surface