# Computations and ML for surjective rational maps

arXiv: https://arxiv.org/abs/2510.08093 · HTML: https://mlsanity.com/paper/2510.08093/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 12 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 1 of 1)

- [Rigor with Machine Learning from Field Theory to the Poincar'e Conjecture](https://mlsanity.com/paper/2402.13321/) (2024)

## Abstract (arXiv)

The present note studies surjective rational endomorphisms f: mathbbP2 dashrightarrow mathbbP2 with cubic terms and the indeterminacy locus If 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 mathbbP2 is surjective if and only if the set If has cardinality at least 3.