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Surjective rational maps and del Pezzo surfaces

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arxiv 2311.01835 v4 pith:6EHBKKZF submitted 2023-11-03 math.AG

Ilya Karzhemanov , Anna Lekontseva This is my paper · ORCID
classification math.AG
keywords pezzorationalsurfacessurjectivebiggercasecertaincondition
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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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  1. Computations and ML for surjective rational maps

    math.AG 2025-10 conditional novelty 6.0 of 10

    A general cubic rational self-map of P^2 is surjective when its indeterminacy locus has at most six points, and two new explicit surjective cubic maps are proved.

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