Stability of a natural sheaf over the cartesian square of the Hilbert\n scheme of points on a K3 surface

2015/06/19 by Eyal Markman, Markman, Eyal
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1506.06191

openalex publication_date 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a K3 surface and S^[n] the Hilbert scheme of length n subschemes of\nS. Over the cartesian square of S^[n] there exists a natural reflexive rank\n2n-2 coherent sheaf E, which is locally free away from the diagonal. The fiber\nof E, over a pair of ideal sheaves of distinct subschemes, is the vector space\nof extensions of the first ideal sheaf by the second. We prove that E is slope\nstable if the rank of the Picard group of S is less than or equal to 19. The\nChern classes of End(E) are known to be monodromy invariant. Consequently, the\nsheaf End(E) is polystable-hyperholomorphic.\n

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