Computations and ML for surjective rational maps

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 $3$.

Algebraic Geometry (math.AG); Machine Learning (cs.LG)

arXiv:2510.08093 [math.AG]

(or arXiv:2510.08093v2 [math.AG] for this version)

https://doi.org/10.48550/arXiv.2510.08093 Focus to learn more arXiv-issued DOI via DataCite

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