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Title:
Rational Hodge isometries of hyper-Kahler varieties of K3[n] and generalized Kummer type are algebraic
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Abstract:
Let X and Y be projective hyper-Kahler manifolds deformation equivalent to the Hilbert scheme of n points on a K3 surface. Let f be a Hodge isometry of the second rational cohomologies of X and Y with respect to the Beauville-Bogomolov-Fujiki pairings. We prove that f is induced by an algebraic correspondence. We furthermore lift f to an algebraic 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. We will also discuss the analogous result for hyperkahler manifolds of generalized Kummer deformation type.
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