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A Counterexample to Beauville's Stability Conjecture

A mix of human-written and AI-generated textHuman understanding: all partsmath.AG — Algebraic Geometry

Contributed by Yi Gu, Lifan Guan ↗

Version 1 / Oct 17, 2026 / CC BY 4.0

Abstract

We construct a morphism f:X→Yf: X\to Y from a genus-two curve to an elliptic curve such that f∗Lf_*\mathcal L is unstable for every $\mathcal L\in\Pic^3(X)$. This gives a counterexample to a conjecture of Beauville.

Provenance statement

This counterexample was generated by the Danus system based on gpt-5.6 sol, then it was revised by the contributors.

Tools used

OpenAI
ChatGPTVersion 5.6-sol

References

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Version history

  1. v1Submitted by Lifan GuanInitial depositCurrentOct 17, 2026