Skew-symmetric matrices and Palatini scrolls
Algebraic Geometry
2009-11-23 v2
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 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).
Keywords
Cite
@article{arxiv.0906.1875,
title = {Skew-symmetric matrices and Palatini scrolls},
author = {Daniele Faenzi and Maria Lucia Fania},
journal= {arXiv preprint arXiv:0906.1875},
year = {2009}
}
Comments
Revised version, to appear in Math. Ann