Localization of plus-one generated arrangements
Elisa Palezzato, Michele Torielli
TL;DR
This paper investigates the algebraic structure of plus-one generated hyperplane arrangements, providing methods to compute associated prime ideals and demonstrating that localizations preserve the plus-one generated property.
Contribution
It introduces a way to compute prime ideals from the intersection lattice and proves that localizations of plus-one generated arrangements remain within the same class.
Findings
Prime ideals can be computed from the intersection lattice.
Localizations of plus-one generated arrangements are also plus-one generated.
The paper advances understanding of the algebraic properties of these arrangements.
Abstract
We study the classes of free and plus-one generated hyperplane arrangements. Specifically, we describe how to compute the associated prime ideals of the Jacobian ideal of such an arrangement from its lattice of intersection. Moreover, we prove that the localization of a plus-one generated arrangement is free or plus-one generated.
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