Symbolic Rees algebras and set-theoretic complete intersections

TL;DR

This paper extends key results on symbolic Rees algebras and set-theoretic complete intersections, demonstrating their Noetherian property for specific classes of ideals such as edge ideals, Fermat ideals, and Jacobian ideals.

Contribution

It generalizes previous results to new classes of ideals, showing their symbolic Rees algebras are Noetherian and the ideals are set-theoretic complete intersections.

Findings

Symbolic Rees algebras of certain ideals are Noetherian.

These ideals are set-theoretic complete intersections.

Applications to edge, Fermat, and Jacobian ideals.

Abstract

In this paper we extend a result of Cowsik on set-theoretic complete intersection and a result Huneke, Morales and Goto and Nishida about Noetherian symbolic Rees algebras of ideals. As applications, we show that the symbolic Rees algebras of the following ideals are Noetherian and the ideals are set-theoretic complete intersections: (a) the edge ideal of a complete graph, (b) the Fermat ideal and (c) the Jacobian ideal of a certain hyperplane arrangement.