Ideals with larger projective dimension and regularity

Jesse Beder, Jason McCullough, Luis Núñez-Betancourt, Alexandra Seceleanu, Bart Snapp, Branden Stone

Abstract: We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given by Caviglia (2004) and McCullough (2011). In particular, we describe a family of three-generated homogeneous ideals, in arbitrary characteristic, whose projective dimension grows asymptotically as a power of the degree of the generators. Highlights ► We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. ► This family subsumes and improves upon constructions given by Caviglia (2004) and McCullough (2011). ► In particular, we describe a family of three-generated homogeneous ideals, in arbitrary characteristic, whose projective dimension grows asymptotically as a power of the degree of the generators.