Holomorphic foliations with locally free tangent sheaf

• Grant number: 14/23594-6
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 01, 2015
• End date: January 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Visiting researcher: Jose Omegar Calvo Andrade
• Visiting researcher institution: Centro de Investigación en Matemáticas A.C., Guanajuato (CIMAT), Mexico
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project, we are going to consider mainly two types of holomorphic foliations: (1) Holomorphic foliations of dimension at least 2, with locally free tangent sheaf, and their deformations; (2) Holomorphic foliations of dimension at least 2, whose normal sheaf has ample determinant and with a compact Kupka connected component of its singularset, with radial transversal type. The main problems we are going to consider are: (1) to find sucient conditions in order to decide when a holomorphic foliation has locally free tangent sheaf; (2) determine when a generic deformation of a holomorphic foliation with locally free tangent sheaf also has locally free tangent sheaf; (3) determine when a foliation with locally free tangent sheaf is rigid; (4) classify the holomorphic vector bundles associated to foliations. (AU)

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

OMEGAR CALVO-ANDRADE; MAURÍCIO CÔRREA; ARTURO FERNÁNDEZ-PÉREZ. On non-Kupka points of codimension one foliations on P-3. Anais da Academia Brasileira de Ciências, v. 88, n. 4, p. 2067-2080, Dez. 2016. (14/23594-6)

CALVO-ANDRADE, OMEGAR. Foliations with a radial Kupka set on projective spaces. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 47, n. 4, p. 1071-1083, DEC 2016. (14/23594-6)

CALVO-ANDRADE, OMEGAR; RODRIGUEZ DIAZ, LAZARO O.; SA EARP, HENRIQUE N.. Gauge theory and G(2)-geometry on Calabi-Yau links. REVISTA MATEMATICA IBEROAMERICANA, v. 36, n. 6, p. 1753-1778, 2020. (14/24727-0, 14/13357-7, 14/23594-6)

CALVO-ANDRADE, OMEGAR; CORREA, MAURICIO; FERNANDEZ-PEREZ, ARTURO. On non-Kupka points of codimension one foliations on P-3. Anais da Academia Brasileira de Ciências, v. 88, n. 4, p. 14-pg., 2016-10-01. (14/23594-6)

OMEGAR CALVO-ANDRADE; MAURÍCIO CÔRREA; ARTURO FERNÁNDEZ-PÉREZ. On non-Kupka points of codimension one foliations on ℙ3. Anais da Academia Brasileira de Ciências, v. 88, n. 4, p. 2067-2080, 2016-12-00. (14/23594-6)

CALVO-ANDRADE, O.; CORREA, M.; FERNANDEZ-PEREZ, A.. Higher codimensional foliations with Kupka singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 28, n. 3, MAR 2017. (14/23594-6)

CALVO-ANDRADE, OMEGAR; CORREA, MAURICIO; JARDIM, MARCOS. Codimension One Holomorphic Distributions on the Projective Three-space. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v. 2020, n. 23, p. 9011-9074, NOV 2020. (14/23594-6, 15/20841-5, 14/14743-8, 16/03759-6)