Rationality of Seshadri constants and the Segre–Harbourne–Gimigliano–Hirschowitz conjecture

@article{Dumnicki2016RationalityOS,
  title={Rationality of Seshadri constants and the Segre–Harbourne–Gimigliano–Hirschowitz conjecture},
  author={Marcin Dumnicki and A. K{\"u}ronya and Catriona Maclean and Tomasz Szemberg},
  journal={Advances in Mathematics},
  year={2016},
  volume={303},
  pages={1162-1170}
}
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References

SHOWING 1-10 OF 16 REFERENCES
On Nagata's Conjecture
Abstract This paper gives an improved lower bound on the degrees d such that for general points p 1 ,…,  p n  ∈  P 2 and m  > 0 there is a plane curve of degree d vanishing at each p i with…
A primer on Seshadri constants
Seshadri constants express the so called local positivity of a line bundle on a projective variety. They were introduced by Demailly. The original idea of using them towards a proof of the Fujita…
Seshadri constants on rational surfaces with anticanonical pencils
Variations on Nagata's Conjecture
In this paper we discuss some variations of Nagata's conjecture on linear systems of plane curves. The most relevant concerns non-effectivity (hence nefness) of certain rays, which we call \emph{good…
ON THE MORI CONE OF BLOW-UPS OF THE PLANE
We discuss some properties of the extremal rays of the cone of effective curves of surfaces that are obtained by blowing up P 2 at points in very general position. The main motivation is to rectify…
Geometric Aspects of Polynomial Interpolation in More Variables and of Waring’s Problem
In this paper I treat the problem of determining the dimension of the vector space of homogeneous polynomials in a given number of variables vanishing with some of their derivatives at a finite set…
Singular hermitian metrics on positive line bundles
The notion of a singular hermitian metric on a holomorphic line bundle is introduced as a tool for the study of various algebraic questions. One of the main interests of such metrics is the…
Interactions of Classical and Numerical Algebraic Geometry
While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his…
A primer on Seshadri constants, Interactions of Classical and Numerical Algebraic Geometry, Proceedings of a conference in honor of A. J. Sommese, held at Notre Dame
  • Contemporary Mathematics
  • 2008
Book Review: Positivity in algebraic geometry. I--II
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