The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K 3 surfaces

2010/09/30 by François Charles, Eyal Markman · 50 citations
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cohomology #Deformation theory #Geometry and complex manifolds #Hilbert scheme #Hilbert–Poincaré series #Holomorphic function #Scheme (mathematics) #Symplectic geometry #math.AG

paper · pdf · doi:10.1112/s0010437x12000607

published in Compositio Mathematica 149(3), 481-494 (Cambridge University Press) · 15 pages, minor changes

arxiv created 2011/01/19 · openalex publication_date 2013/02/07 · openalex created_date 2016/06/24 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05

Abstract

Abstract We prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K 3 surface. The proof involves Verbitsky’s theory of hyperholomorphic sheaves and a study of the cohomology algebra of Hilbert schemes of K 3 surfaces.

Citations

• Fourier-Mukai Transforms in Algebraic Geometry

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