Level 2: Maximal Seshadri constants on arbitrary polarized surfaces

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LEVEL 2 OF 4 · Nagata's conjecture and maximal Seshadri constants

Maximal Seshadri constants on arbitrary polarized surfaces

expertly designed by an internal OpenAI model · released 2026-09-23 · original PDF

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How to play: 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 $\sqrt{L^2/r}$ for every sufficiently large integer r. This resolves positively the qualitative Nagata–Biran conjecture for surfaces.

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