CATALOGUE 063
The generalized Mukai conjecture
This catalogue concerns the generalized Mukai inequality for smooth complex Fano manifolds and the classification at equality. The official list contains one manuscript.
All manuscripts, in official catalogue order
These summaries give the principal scope; consult the cited original results for the complete hypotheses and statements.
Page counts include references. On narrow screens, scroll the table sideways.
| # | Manuscript and overview | Principal claim | Role and available overview |
|---|---|---|---|
| 01 | The generalized Mukai conjecture →Short name: Generalized Mukai2026-09-24 · 19 pagesOriginal paper (GitHub) ↗ | For smooth complex projective Fano varieties, asserts ρ(X)(ι(X)−1) ≤ dim X and characterizes equality by products of projective spaces. Theorem 1.1 · p. 2 ↗ | A descendant lower bound and a recurrence give independent eigenvalues; an alternating trace gives the inequality. Rational-curve families and a product characterization settle equality. Read the proof overview → |
Connections to external results
The input table distinguishes direct inputs from an alternative contraction, with uses, hypotheses, and checking scope. Connections to other catalogues remain incompletely investigated.
Sources and checking scope
Official subject: Algebraic and complex geometry. Catalogue edition: October 6, 2026.
OpenAI Research Catalog · Catalogue 063 · p. 8 · Official manuscript list
Source snapshot: fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
Sections 2–6 and the statements and applications of direct inputs were checked. This is not a complete independent proof verification; remaining checks are listed in the article.