Nagata-Biran conjecture

In mathematics, the Nagata-Biran conjecture is a generalisation of the Nagata conjecture to arbitrary polarised surfaces.

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

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