Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 039-04. Maximal multipoint Seshadri constants in positive characteristic
Manuscript map · lines 3385–3394
OpenAI@2026-10-07#rem:oai-p-039-04
Authors: OpenAI. Family 039.
Title: Maximal multipoint Seshadri constants in positive characteristic.
Abstract: Let L be an ample line bundle on a smooth integral projective variety X over an algebraically closed field of positive characteristic, with ${}dim X=n{}ge3$. We prove that there is a threshold $r_0=r_0(X,L)$ such that for every integer $r{}ge r_0$, the ordinary multipoint Seshadri constant at the geometric generic tuple of r points equals the volume bound $(L{}n/r){}{1/n}$. The same conclusion holds in dimension two. This establishes the positive-characteristic form of the qualitative Nagata–Biran–Szemberg assertion at geometric generic tuples.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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