On the Singular Scheme of Split Foliations

Autor(es)

Correa, Jr., Mauricio ^[1] ; Jardim, Marcos ^[2] ; Martins, Renato Vidal ^[1]

Afiliação do(s) autor(es)

^[1] ICEx UFMG, Dept Matemat, BR-30123970 Belo Horizonte, MG - Brazil

^[2] IMECC UNICAMP, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Indiana University Mathematics Journal; v. 64, n. 5, p. 1359-1381, 2015.
• Citações Web of Science: 1

Resumo

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 2 is birational to a Grassmannian. (AU)

• Processo FAPESP: 14/14743-8 - Feixes em variedades projetivas
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Regular