Geometric aspects of singularities of mappings from the plane to the tridimensional space

• Grant number: 12/22754-4
• Support Opportunities: Scholarships abroad - Research
• Start date: July 01, 2013
• End date: December 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Washington Luiz Marar
• Grantee: Washington Luiz Marar
• Host Investigator: David Mond
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Warwick, England

Abstract

The geometry associated to the singularities of map germs from the plane to the tridimensional space is very reach. The subject can be divided in two cases, namely, mappings of corank 1 and corank 2. The work of David Mond on the corank 1 case is very profound. However, in this project we intend to rewrite some of his results for corank 1 mappings as a 1-parameter family of plane curves and relating Mond's invariants to the codimension 1 singularities of plane curves. This should provide a deeper understand of the geometry of the corank 1 mappings. For the corank 2 mappings, although very hard to deal with when compared to the corank 1 case, we intend to continue our search for a deep understanding of its geometry, particularly for the so called double fold map germs, as in the study initiated by J.J. Nuño-Ballesteros and myself. (AU)