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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.)

Codimension One Holomorphic Distributions on the Projective Three-space

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Author(s):
Calvo-Andrade, Omegar [1] ; Correa, Mauricio [2] ; Jardim, Marcos [3]
Total Authors: 3
Affiliation:
[1] Ctr Invetigac Matemat, Ap Postal 402, Guanajuato 36000, Gto - Mexico
[2] ICEX UFMG, Dept Matemat, Av Antonio Carlos 6627, BR-31270901 Belo Horizonte, MG - Brazil
[3] Univ Estadual Campinas, Dept Matemat, IMECC, Rua Sergio Buarque de Holanda 651, BR-13083970 Campinas, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: INTERNATIONAL MATHEMATICS RESEARCH NOTICES; v. 2020, n. 23, p. 9011-9074, NOV 2020.
Web of Science Citations: 2
Abstract

We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2 with locally free tangent sheaves and show that codimension one distributions of arbitrary degree with only isolated singularities have stable tangent sheaves. Furthermore, we describe the moduli space of distributions in terms of Grothendieck's Quot-scheme for the tangent bundle. In certain cases, we show that the moduli space of codimension one distributions on the projective space is an irreducible, nonsingular quasi-projective variety. Finally, we prove that every rational foliation and certain logarithmic foliations have stable tangent sheaves. (AU)

FAPESP's process: 14/23594-6 - Holomorphic foliations with locally free tangent sheaf
Grantee:Marcos Benevenuto Jardim
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 15/20841-5 - Global geometry of singular holomorphic foliations and distributions
Grantee:Marcos Benevenuto Jardim
Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
FAPESP's process: 14/14743-8 - Sheaves on projective varieties
Grantee:Marcos Benevenuto Jardim
Support Opportunities: Regular Research Grants
FAPESP's process: 16/03759-6 - Moduli spaces of stable objects on the projective space
Grantee:Marcos Benevenuto Jardim
Support Opportunities: Scholarships abroad - Research