Symbolic powers of planar point configurations
Marcin Dumnicki, Tomasz Szemberg, Halszka Tutaj-Gasinska
TL;DR
This paper investigates how the growth of initial degrees of symbolic powers of point ideals in the projective plane reveals geometric properties of the point configurations.
Contribution
It establishes a connection between bounds on symbolic power degrees and the geometric structure of point sets in the projective plane.
Findings
Bounds on symbolic power degrees determine geometric configurations.
Growth rates of degrees reveal special arrangements of points.
Results apply over algebraically closed fields of characteristic zero.
Abstract
We study initial degrees of symbolic powers of ideals of arbitrary finite sets of points in the projective plane over an algebraically closed field of characteristic zero. We show, how bounds on the growth of these degrees determine the geometry of the given set of points.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory