Finitely generated symbolic Rees rings of ideals defining certain finite sets of points in P^2

TL;DR

This paper proves that the symbolic Rees rings of ideals defining specific finite point sets in the projective plane are finitely generated, using Huneke's criterion, contributing to algebraic geometry and commutative algebra.

Contribution

It establishes finite generation of symbolic Rees rings for certain point configurations in P^2 using a ring-theoretic criterion.

Findings

Symbolic Rees rings are finitely generated for specific point sets in P^2.

Utilizes Huneke's criterion to prove finite generation.

Advances understanding of Rees rings in algebraic geometry.

Abstract

The purpose of this paper is to prove that the symbolic Rees rings of ideals defining certain finite sets of points in the projective plane over an algebraically closed field are finitely generated using a ring theoretical criterion which is known as Huneke's criterion.