{"id":"openai-math/Maximal-multipoint-Seshadri-constants-in-positive-characteristic","pdf":"https://github.com/openai/math/blob/main/preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/seshadri-positive-characteristic.pdf","url":"https://github.com/openai/math/tree/main/preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026","tags":["seshadri-constants","positive-characteristic","algebraic-geometry","multipoint"],"score":0,"title":"Maximal multipoint Seshadri constants in positive characteristic","domain":"Algebraic and complex geometry","family":"039","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Nagata’s conjecture and maximal Seshadri constants"}