Nagata–Biran conjecture
# 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

    $\varepsilon (p_{1},\ldots ,p_{r};X,L)={d \over {\sqrt {r}}}.$
