The projective dimension of codimension two algebra presented by quadrics

TL;DR

This paper establishes a precise upper limit on the projective dimension for height two ideals generated by quadrics in polynomial rings, regardless of the number of variables involved.

Contribution

It provides a new sharp upper bound for the projective dimension of codimension two ideals generated by quadrics.

Findings

Sharp upper bound for projective dimension proved

Applicable to polynomial rings with arbitrarily many variables

Advances understanding of algebraic properties of quadratic ideals

Abstract

We prove a sharp upper bound for the projective dimension of ideals of height two generated by quadrics in a polynomial ring with arbitrary large number of variables.