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

• http://mat.ap.krakow.pl/aapc/index.php/studmath/article/viewFile/48/41, page 3 of PDF.

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