Twisted cubics on cubic fourfolds

Abstract : We construct a new twenty-dimensional family of projective eight-dimensional holomorphically symplectic manifolds: the compactified moduli space M_3(Y) of twisted cubics on a smooth cubic fourfold Y that does not contain a plane is shown to be smooth and to admit a contraction M_3(Y) -> Z(Y) to a projective eight-dimensional symplectic manifold Z(Y). The construction is based on results on linear determinantal representations of singular cubic surfaces.
Type de document :
Pré-publication, Document de travail
2013
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https://hal.archives-ouvertes.fr/hal-00819683
Contributeur : Christoph Sorger <>
Soumis le : jeudi 2 mai 2013 - 09:10:35
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

Identifiants

  • HAL Id : hal-00819683, version 1
  • ARXIV : 1305.0178

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IRMA | UNAM | LMJL | FMPL | INSMI

Citation

Christian Lehn, Manfred Lehn, Christoph Sorger, Duco Van Straten. Twisted cubics on cubic fourfolds. 2013. <hal-00819683>

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