Irreducible symplectic 4-folds and Eisenbud-Popescu-Walter sextics
| dc.creator | O'Grady, Kieran G. | |
| dc.date | 2005-07-19 | |
| dc.date.accessioned | 2026-07-07T05:21:51Z | |
| dc.date.available | 2026-07-07T05:21:51Z | |
| dc.description | Eisenbud Popescu and Walter have constructed certain special 4-dimensional sextic hypersurfaces as Lagrangian degeneracy loci. We prove that the natural double cover of a generic EPW-sextic is a deformation of the Hilbert square of a K3-surface and that the family of such varieties is locally complete for deformations that keep the hyperplane class of type (1,1) - thus we get an example similar to that (discovered by Beauville and Donagi) of the Fano variety of lines on a cubic 4-fold. Conversely suppose that X is an irreducible symplectic 4-fold numerically equivalent to the Hilbert square of a K3-surface, that H is an ample divisor on X of square 2 for Beauville's quadratic form and that the map associated to |H| is the composition of the quotient map $X\to Y$ for an anti-symplectic involution on X followed by an immersion of Y; then Y is an EPW-sextic and $X\to Y$ is the natural double cover. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507398 | |
| dc.identifier | http://arxiv.org/abs/math/0507398 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75842 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | Irreducible symplectic 4-folds and Eisenbud-Popescu-Walter sextics | |
| dc.type | text |