Nagata–Biran conjecture

In mathematics, the Nagata–Biran conjecture, named after Masayoshi Nagata and Paul Biran, is a generalisation of Nagata's conjecture on curves to arbitrary polarised surfaces.

Statement

Let X be a smooth algebraic surface and L be an ample line bundle on X of degree d. The Nagata–Biran conjecture states that for sufficiently large r the Seshadri constant satisfies

$\epsilon (p_1,\dots ,p_r;X,L)=\frac{d}{\sqrt{r}}.$

References

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• . See in particular page 3 of the pdf.

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