Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case

Abstract

Let $f:{\mathbb{K}}^n\to {\mathbb{K}}^m$ be a generically finite polynomial map of degree $d$ between affine spaces. In arXiv:1411.5011 we proved that if $\mathbb{K}$ is the field of complex or real numbers, then the set $S_f$ of points at which $f$ is not proper, is covered by polynomial curves of degree at most $d-1$. In this paper we generalize this result to positive characteristic. We provide a geometric proof of an upper bound by $d$.

arXiv admin note: text overlap with arXiv:1501.00223