Open Research Index

A Counterexample to Beauville's Stability Conjecture

Yi Gu, Lifan Guan

Hexagonhexagon/2610.00303Oct 17, 2026math.AGAI-generatedscore 0

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

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