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arXiv · 2510.08093

Computations and ML for surjective rational maps

Ilya Karzhemanov
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Abstract

The present note studies \emph{surjective rational endomorphisms} $f: \mathbb{P}^2 \dashrightarrow \mathbb{P}^2$ with \emph{cubic} terms and the indeterminacy locus $I_f \ne \emptyset$. We develop an experimental approach, based on some Python programming and Machine Learning, towards the classification of such maps; a couple of new explicit $f$ is constructed in this way. We also prove (via pure projective geometry) that a general non-regular cubic endomorphism $f$ of $\mathbb{P}^2$ is surjective if and only if the set $I_f$ has cardinality at least $3$.

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Ilya Karzhemanov. 2025-10-09. Computations and ML for surjective rational maps. https://arxiv.org/abs/2510.08093

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