Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic
arXiv:2204.00516 · doi:10.1112/S0010437X24007048
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.
v2: 45 pages. Added Corollary 1.10 on the algebraic class inducing the Pontryagin product