Constructing Koszul filtrations: existence and non-existence for G-quadratic algebras

Abstract

Given a standard graded algebra over a field, we consider the relationship between G-quadraticity and the existence of a Koszul filtration. We show that having a quadratic Gröbner basis implies the existence of a Koszul filtration for algebras defined by generic determinantal ideals and for algebras defined by binomial edge ideals. We also resolve a conjecture of Ene, Herzog, and Hibi by constructing an example where this implication fails. These results are underpinned by algorithms we develop for constructing Koszul filtrations.

Corrections to section 3, a new section 4, removed previous section 5, and minor edits elsewhere. The new Theorem 3.9 provides a corrected version of the previous Theorem 3.7