EPW-sextics: taxonomy

EPW-sextics: taxonomy

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 do...

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Veröffentlicht in:Manuscripta mathematica 2012-05, Vol.138 (1-2), p.221-272
1. Verfasser: O’Grady, Kieran G.
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Zusammenfassung: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.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-011-0472-7