Fano manifolds of degree ten and EPW sextics

Atanas Iliev; Laurent Manivel

Annales scientifiques de l'École Normale Supérieure (2011)

  • Volume: 44, Issue: 3, page 393-426
  • ISSN: 0012-9593

Abstract

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O’Grady showed that certain special sextics in called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.

How to cite

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Iliev, Atanas, and Manivel, Laurent. "Fano manifolds of degree ten and EPW sextics." Annales scientifiques de l'École Normale Supérieure 44.3 (2011): 393-426. <http://eudml.org/doc/272141>.

@article{Iliev2011,
abstract = {O’Grady showed that certain special sextics in $\mathbb \{P\}^5$ called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.},
author = {Iliev, Atanas, Manivel, Laurent},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {holomorphic symplectic manifold; Fano manifold; grassmannian; Hilbert scheme; conic; double cover; lagrangian surface; integrable system},
language = {eng},
number = {3},
pages = {393-426},
publisher = {Société mathématique de France},
title = {Fano manifolds of degree ten and EPW sextics},
url = {http://eudml.org/doc/272141},
volume = {44},
year = {2011},
}

TY - JOUR
AU - Iliev, Atanas
AU - Manivel, Laurent
TI - Fano manifolds of degree ten and EPW sextics
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2011
PB - Société mathématique de France
VL - 44
IS - 3
SP - 393
EP - 426
AB - O’Grady showed that certain special sextics in $\mathbb {P}^5$ called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.
LA - eng
KW - holomorphic symplectic manifold; Fano manifold; grassmannian; Hilbert scheme; conic; double cover; lagrangian surface; integrable system
UR - http://eudml.org/doc/272141
ER -

References

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