EVENT DETAILS AND ABSTRACT

Title: Syzygies of Veronese variety
Speaker: Michael Kemeny
Speaker Info: University of Wisconsin Madison
Brief Description:
Special Note:
Abstract:

A major pursuit in algebraic geometry for many decades has been syzygies, which is the study of the qualitative features of equations defining algebraic varieties. This topic is by now fairly well developed for curves, where we now have several theorems describing when exactly the syzygy groups vanish, assuming the curve is embedded by a line bundle which is either canonical or sufficiently positive. But we know very little in the higher dimensional case, embarrassingly even in the simplest possible case of projective space embedded by a positive degree line bundle (Veronese varieties). In this case, we do have a good conjecture by Ein-Lazarsfeld predicting exactly when the syzygy groups vanish. I will explain a proof of this conjecture in the case of the two extremal ends of it.