Minimal Whitney stratification and Euler obstruction of discriminants

Author(s)

Barbosa, G. F. ; Grulha, Jr., N. G. ; Saia, M. J.

• Document type: Journal article
• Source: Geometriae Dedicata; v. 186, n. 1, p. 173-180, FEB 2017.
• Web of Science Citations: 1

Abstract

In this work we show how to obtain the minimal Whitney stratification of the discriminant of finitely determined map germs from to , of corank one if , and only with singularities, when with . We apply the theory developed by Gaffney which shows how to compute a Whitney stratification of discriminants of any finitely determined holomorphic map germ in the nice dimensions of Mather, or in its boundary. For the pairs cited above we show that both stratifications coincide. We also compute the local Euler obstruction at 0 in a class of discriminants of finitely determined map germs from to with and only with singularities. (AU)

• FAPESP's process: 13/11258-9 - Topological study on singular varieties and applications on smooth manifolds
• Grantee: Nivaldo de Góes Grulha Júnior
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/00304-2 - Singularities of differentiable mappings: theory and applications
• Grantee: Maria Aparecida Soares Ruas
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/16746-7 - Equisingularity and the Theory of Integral Closure of modules.
• Grantee: Nivaldo de Góes Grulha Júnior
• Support Opportunities: Scholarships abroad - Research