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SUMMARY:Double EPW-sextics - Kieran O'Grady
DTSTART:20140122T141500Z
DTEND:20140122T151500Z
UID:TALK47238@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:The parameter space for lines on a smooth cubic hypersurface i
 n projective 5-space is a hyperkaehler 4-fold deformation equivalent to th
 e Hilbert square of a K3 surface. By varying the cubic we get almost all i
 somomorphism classes of deformations of  the Hilbert square of a K3 surfac
 e equipped with a polarization of Beauville-Bogomolov square 6 and divisbi
 lity 2 \n(these are the two discrete invariants of a primitive polarizatio
 n 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 surfa
 ce equipped with a polarization of Beauville-Bogomolov square 2 (divisibil
 ity is necessarily equal to 1). There exists a family of sextic hypersurfa
 ce in  projective 5-space (EPW-sextics) with 2-dimensional singular set\, 
 which come equipped with a double cover ramified only over the singular se
 t\, such that the family of such double covers parametrizes (up to isomomo
 rphism) almost all deformations  of  the Hilbert square of a K3 surface eq
 uipped with a polarization of Beauville-Bogomolov square 2. We will discus
 s the geometry of double EPW-sextics\, in particular the period map.
LOCATION:MR 13\, CMS
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