Janet Page : An Introduction to Betti Diagrams or: How to Do Better Than Hilbert

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

At

Dec. 3, 2014, 2 p.m.

In

SEO 712

Abstract

We'll start by introducing Betti diagrams for finitely generated graded modules over a polynomial ring, and talking about their relation to the Hilbert function. In the process, we'll define Castelnuovo-Mumford regularity. We'll conclude our discussion by showing that the Betti diagram can give even more geometry than the hilbert function, by working out the example of 7 points in $\mathbb{P}^3$.