Moduli of distributions via singular schemes

Maurício Corrêa (1, 2) , Marcos Jardim (3) , Alan Muniz (4)

1 UFMG - Universidade Federal de Minas Gerais = Federal University of Minas Gerais [Belo Horizonte, Brazil]
2 LEIAM/DEE - Laboratorio de Electrônica Industrial e Acionamento de Máquina
3 UNICAMP - Universidade Estadual de Campinas = University of Campinas
4 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Let X be a smooth projective variety. We show that the map that sends a codimension one distribution on X to its singular scheme is a morphism from the moduli space of distributions into a Hilbert scheme. We describe its fibers and, when X = P-n, compute them via syzygies. As an application, we describe the moduli spaces of degree 1 distributions on P-3. We also give the minimal graded free resolution for the ideal of the singular scheme of a generic distribution on P-3.

Mots clés: Distributions; Hilbert scheme; Singular scheme; Syzygy

Domaines: Mathématiques [math]

Maurício Corrêa, Marcos Jardim, Alan Muniz. Moduli of distributions via singular schemes. Mathematische Zeitschrift, 2022, 301 (3), pp.2709-2731. ⟨10.1007/s00209-022-03001-y⟩. ⟨hal-03887963⟩