Proves the ordinary-double-point volume-gap conjecture: every singular complex algebraic klt germ of dimension n ≥ 2, with zero boundary, has normalized volume at most 2(n-1)^n. Equality holds precisely for an analytic ordinary double point.
Manuscripts (2)
The ordinary-double-point gap in every dimension
September 24, 2026 · source · cite as \cite{OAI:The-ordinary-double-point-gap-in-every-dimension-September-24-2026}
We prove the ordinary-double-point gap conjecture for boundary-zero complex algebraic klt germs in every dimension: a singular n-dimensional germ has normalized volume at most 2(n-1)^n, with equality precisely at an analytic ordinary double point.
The normalized-volume gap in dimension four
September 24, 2026 · source · cite as \cite{OAI:The-normalized-volume-gap-in-dimension-four-September-24-2026}
We prove that every singular complex algebraic klt fourfold germ with zero boundary has normalized volume at most 162, with equality precisely for an analytic ordinary double point. This resolves the ordinary-double-point volume-gap conjecture in dimension four.
Result 037 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md