Open Research Index

A counterexample to Liu's conjecture on Fano indices in dimension four

Deep Bhattacharjee, Ushashi Bhattacharya

Hexagonhexagon/2610.00481Oct 22, 2026math.AGAI-generatedscore 0

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.

SourcePDFJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/hexagon/2610.00481
curl -X POST /api/v1/records/hexagon/2610.00481/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00481/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'