Duke Mathematical Journal
- Duke Math. J.
- Volume 134, Number 1 (2006), 99-137.
Irreducible symplectic -folds and Eisenbud-Popescu-Walter sextics
Eisenbud, Popescu, and Walter  have constructed certain special sextic hypersurfaces in as Lagrangian degeneracy loci. We prove that the natural double cover of a generic Eisenbud-Popescu-Walter (EPW) sextic is a deformation of the Hilbert square of a -surface and that the family of such varieties is locally complete for deformations that keep the hyperplane class of type ; thus we get an example similar to that (discovered by Beauville and Donagi ) of the Fano variety of lines on a cubic -fold. Conversely, suppose that is a numerical , suppose that is an ample divisor on of square for Beauville's quadratic form, and suppose that the map is the composition of the quotient for an antisymplectic involution on followed by an immersion ; then is an EPW sextic, and is the natural double cover
Duke Math. J., Volume 134, Number 1 (2006), 99-137.
First available in Project Euclid: 4 July 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
O'Grady, Kieran G. Irreducible symplectic $4$ -folds and Eisenbud-Popescu-Walter sextics. Duke Math. J. 134 (2006), no. 1, 99--137. doi:10.1215/S0012-7094-06-13413-0. https://projecteuclid.org/euclid.dmj/1152018505