Topological invariants, vanishing Euler characteristic and equisingularities of families of function and analytic variety germs

• Grant number: 12/18805-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 13, 2013
• End date: April 14, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: João Nivaldo Tomazella
• Grantee: João Nivaldo Tomazella
• Visiting researcher: Juan José Nuño Ballesteros
• Visiting researcher institution: Universitat de València, Spain
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The Professor Nuño Ballesteros has keep, for many years, a work partnership with the researchers of the São Carlos's Singularities group. In particular, the partnership between the professors Nuño Balleteros and Tomazella has been productive, resulting, until this moment, in four published papers and in a PHD advised as a join work. This projected intend to continue this partnership. The goals of this project are to verify which properties of the ICIS Milnor number work for the vanishing Euler characteristic of an isolated determinant singularity; to look for the relation relationship between the Bruce Roberts number of a function over an analytic variety and its Milnor number; to get a kind of Varchenko's theorem for the Bruce-Roberts number and a kind of Greuel's theorem for curves. (AU)