Title: Homological algebra on toric varieties

 

Abstract: When studying subvarieties of projective space homological algebra over the standard graded polynomial ring provides several useful tools (free resolutions, syzygies, Castelnuovo-Mumford regularity, etc.) which capture nuanced geometric information. One might hope that there are analogous tools over multigraded polynomial rings, which provide similar geometric information for subvarieties of other toric varieties. I will discuss recent work developing such tools, as well as some of the subtleties that arise when moving to toric varieties beyond projective space. This is joint work with Lauren Cranton Heller and Mahrud Sayrafi.