title: Nagata–Biran conjecture
text: # 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
  
      $\varepsilon (p_{1},\ldots ,p_{r};X,L)={d \over {\sqrt {r}}}.$
  