Skew-symmetric matrices and Palatini scrolls

Details Skew-symmetric matrices and Palatini scrolls Skew-symmetric matrices and Palatini scrolls

2009-06-10

arxiv.org/abs/0906.1875v2

Mathematics

Algebraic Geometry

Revised version, to appear in Math. Ann

Scientific paper

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 greater than 3, this Grassmannian is proved to be birational to the set of pairs (E,Y), where Y is a smooth plane curve of degree k and E is a stable rank-2 bundle on Y whose determinant is O(k-1).

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