{"id":"hexagon/2610.00481","pdf":"https://hexagonmath.org/pdf/2610.00481v1","url":"https://hexagonmath.org/abs/2610.00481v1","tags":["msc:14J32","msc:14B05","msc:14J45","msc:14M25","Calabi–Yau variety","Fano index","index","log canonical singularity","weighted projective space"],"score":0,"title":"A counterexample to Liu's conjecture on Fano indices in dimension four","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"math.AG","summary":"We prove that Liu's conjecture on Fano indices fails in dimension four: $1389$ is the index of a terminal Calabi--Yau fourfold and of a four-dimensional log canonical singularity, but it is not the Fano index of any canonical weighted projective space of dimension four.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}