Homogeneous liaison and the sequentially bounded licci property

Abstract

We consider homogeneously licci ideals in a polynomial ring and focus on the degrees of the forms generating the regular sequences. Using a sequentially bounded condition on these degrees, E. Chong discovered a large class of licci ideals satisfying the Eisenbud–Green–Harris conjecture (among them, grade $3$ Gorenstein ideals). He raised the question of whether these sequentially bounded links were possible for all homogeneously licci ideals. We answer his question in the negative, and in doing so answer a question of C. Huneke and B. Ulrich about strongly licci ideals. The structure of certain Betti tables plays a central role in our proof.