2016/08/20 by Eyal Markman, Markman, Eyal
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.1608.05798
openalex publication_date 2016/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a 2n-dimensional smooth and compact moduli space of stable sheaves\non a K3 surface S and U a universal sheaf over S x M. Over M x M there exists a\nnatural reflexive sheaf E of rank 2n-2, namely the first relative extension\nsheaf of the two pullbacks of U to M x S x M. We prove that E is slope-stable\nwith respect to every Kahler class on M. The sheaf E is known to deform to a\nsheaf E' over X x X, for every manifold X deformation equivalent to M, and we\nprove that E' is slope-stable with respect to every Kahler class on X. This\ntriviality of the stability chamber structure combines with a result of S.\nMehrotra and the author to show that the deformed sheaf E' is canonical.\nConsequently, the pretriangulated K3 category associated to the pair (X x X,E')\nin our earlier work with S. Mehrotra depends only on the isomorphism class of\nX.\n