Session S14 - Global Injectivity, Jacobian Conjecture, and Related Topics

Wednesday, July 14, 12:50 ~ 13:40 UTC-3

Jacobian conjecture via intersection homology

Anna Valette

Jagiellonian University, Poland   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The aim of this talk is to give an approach to the Jacobian conjecture using intersection homology. The main idea is to reduce the study of a given mapping $F:\mathbb{C}^n \to \mathbb{C}^n$ to the study of a singular semi-algebraic set. We will construct a pseudomanifold $N_F$ (i.e. a semi-algebraic subset of $\mathbb{R}^m$ whose singular locus is of codimension at least $2$ in itself and whose regular locus is dense in itself) associated to a given polynomial map $F:\mathbb{C}^n\to\mathbb{C}^n$. We will show that in the case $n=2$, the map $F$ with non-vanishing Jacobian is not proper iff the intersection homology of $N_F$ is nontrivial.

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