Lê-Greuel type formula for the Euler obstruction and applications

Nicolas Dutertre (1) , Nivaldo G. Grulha Jr. (2)

1 I2M - Institut de Mathématiques de Marseille
2 ICMC-USP - Instituto de Ciências Mathemàticas e de Computação [São Carlos]

The Euler obstruction of a function can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we give a version of the Lê-Greuel formula for two germs of analytic functions with isolated singularity at the origin on a singular space. Using this formula and results of Loeser, we also present an integral formula for the Euler obstruction of a function, generalizing a formula of Kennedy.

Keywords: Euler obstruction; Milnor fiber; complex link

Domains: Algebraic Geometry [math.AG]

Nicolas Dutertre, Nivaldo G. Grulha Jr.. Lê-Greuel type formula for the Euler obstruction and applications. Advances in Mathematics, 2014, 251, pp.127-146. ⟨hal-00626791⟩