Ciliberto-Miranda degenerations of ${\mathbb{CP}}^2$ blown up in 10 points

Abstract

We simplify Ciliberto's and Miranda's method(arXiv:0812.0032) to construct degenerations of ${\mathbb{CP}}^2$ blown up in several points yielding lower bounds of the corresponding multi-point Seshadri constants. In particular we exploit an asymptotic result of the author (arXiv:math/0508561) which allows to check the non-specialty of much fewer linear systems on ${\mathbb{CP}}^2$. We obtain the lower bound 117/370 for the 10-point Seshadri constant on ${\mathbb{CP}}^2$.

33 pages, 6 figures

References in corpus (1)

• Homogeneous interpolation on ten points

Cited by in corpus (1)

• Emptiness of homogeneous linear systems with ten general base points