A note on Fr\"oberg's conjecture for forms of equal degrees

TL;DR

This paper proves Fröberg's conjecture for many cases where all generators of the ideal have the same degree, using elementary methods to simplify the problem.

Contribution

It provides a significant extension of known results by settling the conjecture for a broad class of equal-degree forms through elementary considerations.

Findings

Fröberg's conjecture is confirmed for many cases with equal-degree generators.

Elementary methods are effective in addressing complex algebraic conjectures.

The results expand the understanding of ideal generation in polynomial rings.

Abstract

In this note by using elementary considerations, we settle Fr\"oberg's conjecture for a large number of cases, when all generators of ideals have the same degree.