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