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Double EPW-sextics

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  • UserKieran O'Grady
  • ClockWednesday 22 January 2014, 14:15-15:15
  • HouseMR 13, CMS.

If you have a question about this talk, please contact Dr. J Ross.

The parameter space for lines on a smooth cubic hypersurface in projective 5-space is a hyperkaehler 4-fold deformation equivalent to the Hilbert square of a K3 surface. By varying the cubic we get almost all isomomorphism classes of deformations of the Hilbert square of a K3 surface equipped with a polarization of Beauville-Bogomolov square 6 and divisbility 2 (these are the two discrete invariants of a primitive polarization on a deformation of the Hilbert square of a K3). There is an analogous picture if we consider deformations of the Hilbert square of a K3 surface equipped with a polarization of Beauville-Bogomolov square 2 (divisibility is necessarily equal to 1). There exists a family of sextic hypersurface in projective 5-space (EPW-sextics) with 2-dimensional singular set, which come equipped with a double cover ramified only over the singular set, such that the family of such double covers parametrizes (up to isomomorphism) almost all deformations of the Hilbert square of a K3 surface equipped with a polarization of Beauville-Bogomolov square 2. We will discuss the geometry of double EPW -sextics, in particular the period map.

This talk is part of the Algebraic Geometry Seminar series.

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