EPW-sextics: taxonomy

Details EPW-sextics: taxonomy EPW-sextics: taxonomy

2010-07-22

arxiv.org/abs/1007.3882v2

Mathematics

Algebraic Geometry

Improved exposition. Added a result which was only implicit in the first version. Removed Section 3

Scientific paper

An EPW-sextic is a special 4-dimensional hypersurfaces of degree 6 which comes equipped with a double cover which generically is a Hyperkaehler 4-fold deformation equivalent to the Hilbert square of a K3 surface. The family of EPW-sextics is analogous to the family of cubic 4-fold hypersurfaces, more precisely double EPW-sextics are analogous to varieties of lines on cubic 4-folds. This first paper in a series on moduli and periods of double EPW-sextics is mainly concerned with the classification of EPW-sextics which are analogous to cubic 4-folds whose singular locus has strictly positive dimension.

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