On catalecticant perfect ideals of codimension 2

TL;DR

This paper investigates the algebraic properties of catalectic codimension two perfect ideals and their degenerations, focusing on their symbolic powers in a setting with many variables.

Contribution

It introduces a study of linearly presented catalectic ideals with many variables, expanding understanding of their structure and symbolic powers.

Findings

Analysis of symbolic powers of catalectic ideals

Characterization of degenerations of these ideals

Insights into their algebraic structure

Abstract

One deals with catalectic codimension two perfect ideals and certain degenerations thereof, with a view towards the nature of their symbolic powers. In the spirit of [10] one considers linearly presented such ideals, only now in the situation where the number of variables is sufficiently larger than the size of the matrix, yet still stays within reasonable bounds.