Mathematics Research Institute

Seminario
Seminario

On the Singular Scheme of Split Foliations

Mauricio Corrêa Jr (UFMG, Belo Horizonte)

Fecha: 16/12/2013 13:00
Lugar: Sala A125, Facultad de Ciencias
Grupo: ECSING

Abstract:
We prove that the tangent sheaf of a codimension one locally free distribution splits as a sum of line bundles if and only if its singular scheme is arithmetically Cohen-Macaulay. In addition, we show that a foliation by curves is given by an intersection of generically transversal holomorphic distributions of codimension one if and only if its singular scheme is arithmetically Buchsbaum. Finally, we establish that these foliations are determined by their singular schemes, and deduce that the Hilbert scheme of certain arithmeticall y Buchsbaum schemes of codimension 2 is birational to a Grassmannian.