Remark: Family 039. Nagata's conjecture and maximal Seshadri constants

Proves Nagata's strict inequality ${\sum }_i{m}_i<d\sqrt{r}$ for every nonzero effective plane curve of degree $d$ through $r\ge 10$ very general complex points, with arbitrary multiplicities $m_i$. It also proves maximal multipoint Seshadri constants $(L^n/r{)}^{1/n}$ for every smooth polarized projective variety of dimension $n\ge 2$ and all sufficiently large $r$: at very general points over $\mathbb{C}$, and at the geometric generic tuple over any algebraically closed field of positive characteristic.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.