On the resolution of fan algebras of principal ideals over a Noetherian ring

TL;DR

This paper constructs an explicit minimal resolution for fan algebras of principal ideals over a Noetherian ring when the fan is a rational cone in the plane, providing new insights into their algebraic structure.

Contribution

It provides an explicit construction of a minimal resolution for fan algebras of principal ideals in a specific geometric setting, which was not previously known.

Findings

Explicit minimal resolution constructed for fan algebras

Resolution applies to fan cones in the plane

Under mild conditions, the resolution is minimal

Abstract

We construct explicitly a resolution of a fan algebra of principal ideals over a Noetherian ring for the case when the fan is a proper rational cone in the plane. Under some mild conditions on the initial data, we show that this resolution is minimal.