Eisenbud and Goto described the Castelnuovo-Mumford regularity of a module on projective space in terms of three different properties of the corresponding graded module: its betti numbers, its local cohomology, and its truncations. For the multigraded generalization of regularity defined by Maclagan and Smith, these three conditions are no longer equivalent. I will characterize each of them for modules on products of projective spaces.
Multigraded regularity on products of projective spaces
Juliette Bruce, University of California, BerkeleyAuthors: Juliette Bruce, Lauren Cranton Heller, Mahrud Sayrafi
2022 AWM Research Symposium
Homological and Combinatorial Aspects of Commutative Algebra