{"id":"openai-math/The-ordinary-double-point-gap-in-every-dimension","pdf":"https://github.com/openai/math/blob/main/preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026","tags":["algebraic-geometry","klt-singularities","normalized-volume"],"score":0,"title":"The ordinary-double-point gap in every dimension","domain":"Algebraic and complex geometry","family":"037","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The ordinary-double-point volume gap"}