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- W1647842522 abstract "T. Szemberg proposed in 2001 a generalization to arbitrary varieties of M. Nagata's 1959 open conjecture, which claims that the Seshadri constant of r>9 very general points of the projective plane is maximal. Here we prove that Nagata's original conjecture implies Szemberg's for all smooth surfaces X with an ample divisor L generating its Neron-Severi group and such that L^2 is a square. More generally, we prove that the (n-1)-dimensional Seshadri constant of an ample divisor L on a projective variety X of dimension n at r very general points is bounded below by the product of the (n-1)-dimensional Seshadri constant of at a very general point times the (n-1)-dimensional Seshadri constant of the hyperplane on projective n-space at r very general points." @default.
- W1647842522 created "2016-06-24" @default.
- W1647842522 creator A5056915259 @default.
- W1647842522 date "2003-04-09" @default.
- W1647842522 modified "2023-09-27" @default.
- W1647842522 title "On the Nagata conjecture" @default.
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