Abstract
An EPW-sextic is a special 4-dimensional hypersurfaces of degree 6 which comes equipped with a double cover which generically is a Hyperkähler 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-folds, more precisely double EPW-sextics are analogous to varieties of lines on cubic 4-folds. In this paper we are 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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