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 P(2k-1). For m = 3 and k > 3, this Grassmannian is proved to be birational to the set of pairs (epsilon, Y), where Y is a smooth plane curve of degree k and epsilon is a stable rank-2 bundle on Y whose determinant is O(Y) (k - 1).

Skew-symmetric matrices and Palatini scrolls

FANIA, Maria Lucia
2010-01-01

Abstract

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 P(2k-1). For m = 3 and k > 3, this Grassmannian is proved to be birational to the set of pairs (epsilon, Y), where Y is a smooth plane curve of degree k and epsilon is a stable rank-2 bundle on Y whose determinant is O(Y) (k - 1).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/18678
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