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Article Dans Une Revue Mathematische Annalen Année : 2010

Skew-symmetric matrices and Palatini scrolls

Résumé

We prove that, for m greater than 3 and k greater than m - 2, the Grassmannian of m-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension 2k is birational to the Hilbert scheme of Palatini scrolls in P2k-1. For m = 3 and k > 3, this Grassmannian is proved to be birational to the set of pairs (ε, Y), where Y is a smooth plane curve of degree k and ε is a stable rank-2 bundle on Y whose determinant is oscriptY(k-1). © Springer-Verlag 2009.

Dates et versions

hal-00865081 , version 1 (23-09-2013)

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Daniele Faenzi, M.L. Fania. Skew-symmetric matrices and Palatini scrolls. Mathematische Annalen, 2010, 347 (4), pp.859-883. ⟨10.1007/s00208-009-0450-5⟩. ⟨hal-00865081⟩
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