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arXiv · 0802.0925

Regularity and non-emptyness of linear systems in $\mathbb P^n$

Marcin Dumnicki
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Abstract

The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in $\mathbb P^n$) passing through multiple points in general position. To do the above we formulate and prove new theorem, which allows to show non-specialty of linear system by splitting it into non-special (and simpler) systems. As a result we give new bounds for multiple point Seshadri constants on $\PP^2$.

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Marcin Dumnicki. 2008-02-07. Regularity and non-emptyness of linear systems in $\mathbb P^n$. https://arxiv.org/abs/0802.0925

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