{"ID":2858095,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08093","arxiv_id":"2510.08093","title":"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 $3$.","short_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...","url_abs":"https://arxiv.org/abs/2510.08093","url_pdf":"https://arxiv.org/pdf/2510.08093v1","authors":"[\"Ilya Karzhemanov\"]","published":"2025-10-09T11:27:10Z","proceeding":"math.AG","tasks":"[\"math.AG\",\"cs.LG\"]","methods":"[]","has_code":false}