Rees algebras of ideals of star configurations

TL;DR

This paper investigates the algebraic structure of Rees algebras associated with ideals from star configurations, providing characterizations of their properties and explicit descriptions in specific cases.

Contribution

It characterizes when these ideals are of linear and fiber type and explicitly describes the defining ideal for height two star configurations.

Findings

Identifies conditions for ideals to be of linear type.

Provides sufficient conditions for ideals to be of fiber type.

Gives a complete description of the defining ideal for height two star configurations.

Abstract

In this article we study the defining ideal of Rees algebras of ideals of star configurations. We characterize when these ideals are of linear type and provide sufficient conditions for them to be of fiber type. In the case of star configurations of height two, we give a full description of the defining ideal of the Rees algebra, by explicitly identifying a minimal generating set.