Characterizing multigraded regularity on products of projective spaces

Algebra Student Seminar
Friday, October 15, 2021 - 10:00am for 1 hour (actually 50 minutes)
Skiles 005
Mahrud Sayrafi – University of Minnesota –
Marc Härkönen

Motivated by toric geometry, Maclagan-Smith defined the multigraded Castelnuovo-Mumford regularity for sheaves on a simplicial toric variety. While this definition reduces to the usual definition on a projective space, other descriptions of regularity in terms of the Betti numbers, local cohomology, or resolutions of truncations of the corresponding graded module proven by Eisenbud and Goto are no longer equivalent. I will discuss recent joint work with Lauren Cranton Heller and Juliette Bruce on generalizing Eisenbud-Goto's conditions to the "easiest difficult" case, namely products of projective spaces, and our hopes and dreams for how to do the same for other toric varieties.