An asymptotic version of Dumnicki's algorithm for linear systems in $\mathbb{CP}^2$

Details An asymptotic version of Dumnicki's algorithm for linear systems in $\mathbb{CP}^2$ An asymptotic version of Dumnicki's algorithm for linear systems in $\mathbb{CP}^2$

2008-01-18

arxiv.org/abs/0801.2926v2

Mathematics

Algebraic Geometry

14 pages, 5 figures, references added

Scientific paper

Using Dumnicki's approach to showing non-specialty of linear systems consisting of plane curves with prescribed multiplicities in sufficiently general points on $\mathbb{P}^2$ we develop an asymptotic method to determine lower bounds for Seshadri constants of general points on $\mathbb{P}^2$. With this method we prove the lower bound 4/13 for 10 general points on $\mathbb{P}^2$.

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