On the Hilbert scheme of degeneracy loci of twisted differential forms

Fabio Tanturri (1, 2)

1 Universität des Saarlandes [Saarbrücken]
2 I2M - Institut de Mathématiques de Marseille

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

Domaines: Géométrie algébrique [math.AG]

Fabio Tanturri. On the Hilbert scheme of degeneracy loci of twisted differential forms. Transactions of the American Mathematical Society, 2016, ⟨10.1090/tran/6637⟩. ⟨hal-01263513⟩