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

Kieran G. O'Grady

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

Algebraic Geometry 2007-05-23 v3 Differential Geometry

Authors: Kieran G. O'Grady

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.

Keywords

irreducible symplectic 4-fold Hilb^2(K3) cup product deformation double cover sextic hypersurface birational

Cite

@article{arxiv.math/0504434,
  title  = {Irreducible symplectic 4-folds numerically equivalent to Hilb^2(K3)},
  author = {Kieran G. O'Grady},
  journal= {arXiv preprint arXiv:math/0504434},
  year   = {2007}
}

Comments

We eliminated the last section because we have solved (in another paper) the problem that was discussed in that section. We added Propositions (3.7) and (4.8)

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

Abstract

Keywords

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