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arXiv · 2204.00516

Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic

Eyal Markman
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Abstract

Let X and Y be compact hyper-Kahler manifolds deformation equivalence to the Hilbert scheme of length n subschemes of a K3 surface. A cohomology class in their product XxY is an analytic correspondence, if it belongs to the subring generated by Chern classes of coherent analytic sheaves. Let f be a Hodge isometry of their second rational cohomologies with respect to the Beauville-Bogomolov-Fujiki pairings. We prove that f is induced by an analytic correspondence. We furthermore lift f to an analytic correspondence F between their total rational cohomologies, which is a Hodge isometry with respect to the Mukai pairings, and which preserves the gradings up to sign. When X and Y are projective the correspondences f and F are algebraic.

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Eyal Markman. 2022-04-01. Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic. https://doi.org/10.1112/s0010437x24007048

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