Alex Stathis : Brill-Noether Loci on the Projective Plane and an Intersection Number

Posted by Tim Ryan , part of the Graduate Algebraic Geometry Seminar.

At

Aug. 27, 2014, 2 p.m.

In

SEO 427

Abstract

We'll begin by recalling the basic properties of the Hilbert scheme of points in the projective plane, and then discuss its Picard group and its generators. We'll then define Brill-Noether divisors and use these to compute some top intersection numbers of the generators. We'll also briefly discuss volumes of divisors and their relation to top intersection numbers. If we have time, we'll discuss some of interesting geometric observations we can make using these numbers.