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Irreducible symplectic 4-folds numerically equivalent to Hilb^2(K3)

Kieran G. O'Grady
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Abstract

First steps towards a classification of irreducible symplectic 4-folds whose integral 2-cohomology with 4-tuple cup product is isomorphic to that of Hilb^2(K3). We prove that any such 4-fold deforms to an irreducible symplectic 4-fold of Type A or Type B. A 4-fold of Type A is a double cover of a (singular) sextic hypersurface and a 4-fold of Type B is birational to a hypersurface of degree at most 12. We conjecture that 4-folds of Type B do not exist.

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Kieran G. O'Grady. 2005-07-19. Irreducible symplectic 4-folds numerically equivalent to Hilb^2(K3). https://arxiv.org/abs/math/0504434

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