IUMJ

Title: On the singular scheme of split foliations

Authors: Marcos Jardim, Mauricio Correa Jr. and Renato Vidal Martins

Issue: Volume 64 (2015), Issue 5, 1359-1381

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 arithmetically Buchsbaum schemes of codimension two is birational to a Grassmannian.