The Jelonek set and the Chern classes of singular varieties

Abstract

This post-doctoral project has two parts. The first part concerns the conjectures and questions which are still open in my Ph. D thesis. This part continues the study of the asymptotic set of a dominant polynomial mapping F: Cn to Cn, which is stratified by the method of the ``ways''(façons) and characterized in some particular cases in my thesis. This study is connected to the Jacobian Conjecture. The second part concerns the Chern classes of the singular varieties defined by Marie-Hélène Schwartz as the obstruction to the construction of so-called ``radial" stratified frames. The construction is relatively complicated and requires fine and delicate techniques. The idea, initialized by T. Mostowski, is to build the ``Lipschitz" frames satisfying the adequate properties such that their obstruction allows to define the characteristic classes of singular varieties.