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arXiv · 2311.01835

Surjective rational maps and del Pezzo surfaces

Ilya Karzhemanov·Anna Lekontseva
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Abstract

We study surjective (not necessarily regular) rational endomorphisms $f$ of smooth del Pezzo surfaces $X$. We prove that under certain natural non\,-\,degeneracy condition $f$ can have degree bigger than $1$ only when $(-K_X^2) > 5$. Some structural properties of $f$ in the case $X = \p^2$ are also established.

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Ilya Karzhemanov, Anna Lekontseva. 2023-11-03. Surjective rational maps and del Pezzo surfaces. https://arxiv.org/abs/2311.01835

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