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arXiv · 1906.06160

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

Zbigniew Jelonek·Michał Lasoń
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Abstract

Let $f:\mathbb{K}^n\rightarrow\mathbb{K}^m$ 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 $d$.

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Zbigniew Jelonek, Michał Lasoń. 2019-06-12. Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case. https://doi.org/10.1142/s0219498820501923

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