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

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 $\PP^2$.

11 pages, 2 figures

References in corpus (2)

• Computing multi-point Seshadri constants on P2
• Seshadri constants via Lelong numbers

Cited by in corpus (5)

• Emptiness of homogeneous linear systems with ten general base points
• Symbolic powers of ideals of generic points in P^3
• Containments of symbolic powers of ideals of generic points in $\PP^3$
• Postulation of general quartuple fat point schemes in P^3
• Postulation of general quintuple fat point schemes in P^3