Double EPW-sextics

Add to your list(s) Download to your calendar using vCal

• Kieran O'Grady
• Wednesday 22 January 2014, 14:15-15:15
• MR 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.

This talk is included in these lists:

• Algebraic Geometry Seminar
• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR 13, CMS
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.