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.

arXiv commentCorrections 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