{"id":"hexagon/2610.00384","pdf":"https://hexagonmath.org/pdf/2610.00384v1","url":"https://hexagonmath.org/abs/2610.00384v1","tags":["math.AG","msc:13A15","msc:13H05","msc:13N05","Eisenbud–Mazur conjecture","Symbolic powers","Veronese surface","critical values","formal curves"],"score":0,"title":"A counterexample to the Eisenbud–Mazur conjecture","domain":"math.AC","origin":"ai-generated","source":"hexagon","authors":["Chung Pang Mok","Yiqi Xu"],"reviews":0,"subject":"math.AC","summary":"We construct a height-five prime ideal $P$ in the six-variable formal power series ring $R$ over $\\mathbb{Q}$ such that $P^{(2)}\\not\\subseteq\\mathfrak{m}P$, thus providing a prime-ideal counterexample to the Eisenbud--Mazur conjecture (with $\\mathbb{Q}$ being the coefficient field). The ideal is the kernel of an explicit quadratic parametrization over a number field of degree $28$ over $\\mathbb{Q}$. A witness has order three, with leading term the determinant of a symmetric $3\\times3$ matrix. We construct the witness by eliminating critical values to all orders and then straightening the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Fable"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}