Regularity and non-emptyness of linear systems in \mathbb Pⁿ

2008/02/07 by Marcin Dumnicki, Dumnicki, Marcin · 3 citations
Computer Science · Mathematics · #13P10 #14H50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0802.0925

openalex publication_date 2008/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Pⁿ) 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 \PP².

Citations

• Seshadri constants via Lelong numbers

Cited by

• Emptiness of homogeneous linear systems with ten general base points
• On divisorial (i) classes
• Symbolic powers of ideals of generic points in P³

Related

• Linear systems in P³ with low degrees and low multiplicities
• Linear families of smooth hypersurfaces over finitely generated fields
• A counterexample to a conjecture on linear systems on P³
• New methods for determining speciality of linear systems based at fat points in Pⁿ
• An asymptotic version of Dumnicki's algorithm for linear systems in \mathbbCP²