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Milnor classes and polar varieties

Grant number: 11/20082-6
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): March 06, 2012
Effective date (End): March 05, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Maria Aparecida Soares Ruas
Grantee:Nancy Carolina Chachapoyas Siesquén
Supervisor abroad: Jean-Paul Michel Ildephonse Brasselet
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Research place: Institut de Mathématiques de Luminy, France  
Associated to the scholarship:10/09736-1 - Milnor classes and polar varieties, BP.DR


The aim of this project is the study of characteristic classes of singular varieties, with emphasis on the study of the difference between the Schwartz-MacPherson classes and Fulton classes. This difference is called the Milnor classe, since it coincides with the Milnor number in the case of complete intersections with isolated singularities.The goal is to combine the techniques that the group of singularities of ICMC-USP has used in the local study of singularities, to the more global methods of algebraic topology and algebraic geometry, to study the following questions about Milnor classes:(1) to study the formulation for Milnor classes in terms of polar varieties, introduced by J.P. Brasselet, initially for singularities which admit stratification with a maximum of three strata;(2) interpret the difference between the Schwartz-Macpherson classes and Fulton classes, in the special case of determinantal singularities. These singularities have been studied by the local group. The goal is to find relations between the Milnor classes and other invariants of the determinantal singularities, such as the Milnor number.(3) proposer, if possible its own definition of Milnor class, which coincides with the difference between the Schwartz-Macpherson classes, and Fulton classes. The project includes a Double Diploma Program of the student, through an agreement between the University of São Paulo and the Université de la Méditerranée, Marseille, with guidance on the French side Prof. Jean-Paul Brasselet. The professor Brasselet is an expert in the study of the topology of singularities, which maintains an important exchange with the ICMC-USP, for about 20 years. (AU)

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Scientific publications
(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)
CHACHAPOYAS SIESQUEN, NANCY CAROLINA. Euler obstruction of essentially isolated determinantal singularities. Topology and its Applications, v. 234, p. 166-177, . (10/09736-1, 11/20082-6)
BRASSELET, JEAN-PAUL; CHACHAPOYAS, NANCY; RUAS, MARIA A. S.. Generic sections of essentially isolated determinantal singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 28, n. 11, . (10/09736-1, 14/00304-2, 15/06697-9, 11/20082-6)

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