{"id":"hexagon/2610.00303","pdf":"https://hexagonmath.org/pdf/2610.00303v1","url":"https://hexagonmath.org/abs/2610.00303v1","tags":["msc:14H60","msc:14H40","msc:14K02","Direct images","Frey–Kani construction.","stability"],"score":0,"title":"A Counterexample to Beauville's Stability Conjecture","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Yi Gu","Lifan Guan"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-17","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}