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

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

2005-04-21

arxiv.org/abs/math/0504434v3

Mathematics

Algebraic Geometry

We eliminated the last section because we have solved (in another paper) the problem that was discussed in that section. We ad

Scientific paper

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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