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The standard conjectures for holomorphic symplectic varieties deformation equivalent to Hilbert schemes of K3 surfaces

Part of: Surfaces and higher-dimensional varieties Global differential geometry Cycles and subschemes

Published online by Cambridge University Press:  07 February 2013

François Charles  and
Eyal Markman
François Charles
Affiliation:
Département de Mathématiques et Applications, École Normale Supérieure, 45, rue d’Ulm, 75005 Paris, France (email: francois.charles@ens.fr, francois.charles@univ-rennes1.fr)
Eyal Markman
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA (email: markman@math.umass.edu)
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Abstract

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We prove the standard conjectures for complex projective varieties that are deformations of the Hilbert scheme of points on a K3 surface. The proof involves Verbitsky’s theory of hyperholomorphic sheaves and a study of the cohomology algebra of Hilbert schemes of K3 surfaces.

Keywords

algebraic cyclesholomorphic symplectic varietiesstandard conjectures

MSC classification

Secondary: 14C25: Algebraic cycles 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli 53C26: Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 3 , March 2013 , pp. 481 - 494
Copyright
Copyright © 2013 The Author(s)

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