Nagata–Biran conjecture

In mathematics, the Nagata–Biran conjecture, named after Masayoshi Nagata and Paul Biran, 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

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

References

• Syzdek, Wioletta (2007), "Submaximal Riemann-Roch expected curves and symplectic packing", Annales Academiae Paedagogicae Cracoviensis 6: 101–122, MR 2370584. See in particular page 3 of the pdf.