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Stable Algebraic Families for P2\mathbb{P}^2

Primarily AI-generated textHuman understanding: some partsmath.DS — Dynamical Systemsmath.AG — Algebraic Geometry

Contributed by Jit Wu Yap ↗

Version 1 / Oct 14, 2026 / CC BY 4.0

Abstract

We classify one-dimensional families of endomorphisms on P2\mathbb{P}^2 that are algebraically stable, generalizing a theorem of McMullen. The non-isotrivial families are either homogeneous lifts of flexible Lattes maps on P1\mathbb{P}^1, or a family of Lattes maps arising from abelian surfaces.

Provenance statement

This was produced after roughly 100 consecutive prompts of GPT6 Astra Ultra with minimal guidance from a human, except to remind GPT to focus on tackling the essential difficulties and to not get distracted. The general idea of the proof is sound but the details are very technical. I hope to write a proper exposition of this in the future.

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Version history

  1. v1Submitted by Jit Wu YapInitial depositCurrentOct 13, 2026