We prove that, for 3 < m < n − 1, the Grassmannian of mdimensional subspaces of the space of skew-symmetric forms over a vector space of dimension n is birational to the Hilbert scheme of degeneracy loci of m global sections of Ωℙn−1 (2), the twisted cotangent bundle on ℙn−1. For 3 = m < n − 1 and n odd, this Grassmannian is proved to be birational to the set of Veronese surfaces parameterized by the Pfaffians of linear skewsymmetric matrices of order n.

On the Hilbert scheme of degeneracy loci of twisted differential forms

Fabio Tanturri
2016

Abstract

We prove that, for 3 < m < n − 1, the Grassmannian of mdimensional subspaces of the space of skew-symmetric forms over a vector space of dimension n is birational to the Hilbert scheme of degeneracy loci of m global sections of Ωℙn−1 (2), the twisted cotangent bundle on ℙn−1. For 3 = m < n − 1 and n odd, this Grassmannian is proved to be birational to the set of Veronese surfaces parameterized by the Pfaffians of linear skewsymmetric matrices of order n.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/1012453
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