Pure Mathematics Seminar: Artie Prendergast

Artie Prendergast, Loughborough University

Wednesday 05 February 2014, 1500-1600
A54, Postgraduate Statistics Centre Lecture Theatre

Positivity and cones in algebraic geometry

Positivity is one of the defining features of algebraic geometry. On an algebraic variety, the set of positive subvarieties forms a convex cone, and the structure of this cone encodes valuable geometric information about the variety. For general varieties these cones can be very difficult to describe, but a remarkable conjecture of Morrison--Kawamata would give a clear picture for varieties of non-negative curvature. In this talk, I will explain what the conjecture predicts, and discuss some results in this direction.