Tim Ryan : A Basic Introduction to Birational Geometry or: How I Spend My Time

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

At

Nov. 12, 2014, 2 p.m.

In

SEO 712

Abstract

I will give a very basic introduction to elements of birational geometry. All grad students are welcome; a basic knowledge of divisors on varieties is the only prerequisite(come talk to me if that is an issue). I will define various cones in the Neron-Severi space including why we care about these cones. Next I will describe some current methods of computing these cones. I will finish with a few examples of these methods, focusing on the Hilbert schemes of points on $\mathbb {P}^2$ and, time permitting, $\mathbb {P}^1 \times \mathbb {P}^1$.