OpenAI · 039-02 · 2026-09-23 · Algebraic and complex geometry
Maximal Seshadri constants on arbitrary polarized surfaces
preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026
Family 039. Nagata's conjecture and maximal Seshadri constants.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Nagata's strict inequality for every nonzero effective plane curve of degree through very general complex points, with arbitrary multiplicities . It also proves maximal multipoint Seshadri constants for every smooth polarized projective variety of dimension and all sufficiently large : at very general points over , and at the geometric generic tuple over any algebraically closed field of positive characteristic.
We prove that, for every smooth integral complex projective surface S and every ample line bundle L, the multipoint Seshadri constant at r very general points equals for every sufficiently large integer r. This resolves positively the qualitative Nagata–Biran conjecture for surfaces.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 039: Nagata’s conjecture and maximal Seshadri constants. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.