Geometry Seminar

Date: October 7, 2019

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Matthew Ballard, University of South Carolina

Title: Can the derived category detect rationality?

Abstract: Rationality questions and the structure of derived categories of coherent sheaves have been shown to be intimately tied together over the past 30 years - both via evidence and tantalizing conjectures. Perhaps the most basic question one can ask is: are there natural conditions on D(X) which would imply the rationality of X? One of the simplest structural conditions on D(X) is that it can be broken into pieces that are derived categories of (smooth) points. In joint work with Duncan, Lamarche, and McFaddin, we show that this is insufficient to guarantee the existence of a k-point in general much less rationality. However if one assumes all the points are just Spec k then we verify this guarantees rationality for toric varieties.