Homogeneous Liaison and the Sequentially Bounded Licci Property

Abstract: In CI-Liaison, significant effort has been made to study ideals that are in the linkage class of a complete intersection, which are called licci ideals. In a polynomial ring, recently E. Chong defined a "sequentially bounded" condition on the degrees of the forms generating the regular sequences, and used this condition to find a large class of licci ideals satisfying the Eisenbud-Green-Harris Conjecture (among them, grade $3$ homogeneous Gorenstein ideals). He raised the question of whether all homogeneous licci ideals are sequentially bounded licci. In this paper we construct a class of examples that are homogeneously licci, but not sequentially bounded licci, thus answering his question in the negative. The structure of certain Betti tables plays a central role in our proof.