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

Wednesday, July 14, 14:50 ~ 15:40 UTC-3

A note on the Jacobian conjecture

Zbigniew Jelonek

Polska Akademia Nauk, Poland   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Let $F:\mathbb{C}^n\to\mathbb{C}^n$ be a polynomial mapping with a non-vanishing Jacobian. If the set $S_F$ of non-properness of $F$ is smooth, then $F$ is a surjective mapping. Moreover, if $S_F$ is connected, then $\chi(S_F)>0.$ Additionally, if $n=2$, then the set $S_F$ of non-properness of $F$ cannot be a curve without self-intersections.

View abstract PDF