CATALOGUE 038
Fujita's freeness conjecture
This catalogue concerns global generation of adjoint bundles on smooth projective complex varieties at the sharp dimension-dependent exponent. The official catalogue contains one manuscript.
The paper 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 | Fujita’s freeness conjecture →Short name: Fujita freeness2026-09-23 · 25 pagesOriginal paper (GitHub) ↗ | For a smooth connected projective complex n-fold and ample L, K_X+mL is globally generated for every integer m≥n+1. Theorem 1.1 · p. 1; Corollary 6.3 · p. 23 ↗ | Exponential minimization, uniform restriction-image estimates, and lifting from local discrepancies. The overview covers the full proof, point centers, the equality divisor, and every higher exponent. Read the proof overview → |
Connections to external results
Start with the complete proof route, then follow exclusion of positive-dimensional centers, isolation of the equality divisor, and extension to every exponent. The last step uses a product with projective space and does not assume global generation of L itself.
The input list distinguishes direct inputs from semicontinuity, vanishing, Brunn–Minkowski and SNC resolution from the methodological reference to Fujita’s local lifting argument. All cross-catalogue dependencies remain uninvestigated.
Sources and checking scope
The official subject is Algebraic and complex geometry. The source is the research catalogue dated October 6, 2026, at fixed commit fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
OpenAI Research Catalog · Catalogue 038 · p. 5
The manuscript is by OpenAI, dated September 23, 2026, and has 25 pages including references. The article and original state the hypotheses and quantifiers explicitly.
Theorem 1.1 · p. 1; Corollary 6.3 · p. 23
The proof text and the statements and application sites of direct external inputs were compared. This is not independent verification of the entire proof. The article’s closing scope statement identifies the external proofs and technical estimates not subjected to complete independent reconstruction or formal verification.