Ideals generated by power sums

TL;DR

This paper studies ideals generated by power sum polynomials in polynomial rings, establishing conditions for these ideals to define complete intersections, normal domains, and UFDs, and resolving a significant case of a related conjecture.

Contribution

It provides new criteria for when ideals generated by power sums form complete intersections, normal domains, or UFDs, and proves a key case of a conjecture in the field.

Findings

Conditions for ideals to define complete intersections

Criteria for normality and UFD properties

Resolution of a key case of a conjecture

Abstract

We consider ideals in a polynomial ring generated by collections of power sum polynomials, and obtain conditions under which these define complete intersection rings, normal domains, and unique factorization domains. We also settle a key case of a conjecture of Conca, Krattenthaler, and Watanabe, and prove other results in that direction.