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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the Singular Scheme of Split Foliations

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Author(s):
Correa, Jr., Mauricio [1] ; Jardim, Marcos [2] ; Martins, Renato Vidal [1]
Total Authors: 3
Affiliation:
[1] ICEx UFMG, Dept Matemat, BR-30123970 Belo Horizonte, MG - Brazil
[2] IMECC UNICAMP, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Indiana University Mathematics Journal; v. 64, n. 5, p. 1359-1381, 2015.
Web of Science Citations: 1
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 2 is birational to a Grassmannian. (AU)

FAPESP's process: 14/14743-8 - Sheaves on projective varieties
Grantee:Marcos Benevenuto Jardim
Support Opportunities: Regular Research Grants