Algebraic Geometry Seminar

Simple SODs => rationality is a mantra that frequently appears in derived categories. Kuznetsov's conjecture for cubic fourfolds is a particular well-known incarnation. For X a variety over a field k, the simplest SODs are full exceptional collections, where D(X) is glued together from copies of points, D(vect k). Orlov conjectures that varieties with full exceptional collections are indeed k-rational. This talk will be focused on two questions: Is Orlov's conjecture true? How sharp is it? The answers, yes in some new cases and quite sharp, come from joint work with Alexander Duncan (UofSC), Alicia Lamarche (Utah), and Patrick McFaddin (Fordham). Speaker(s): Matthew Ballard (University of South Carolina and University of Michigan)