Chow ring 1. Introduction.
Channel: Richard E Borcherds
Date: 2020-12-01

This lecture gives an introductory overview of the Chow ring of a nonsingular variety. The idea is to define a ring structure related to subvarieties with the product corresponding to intersection. There are several complications that have to be solved, in particular how to define intersection multiplicities and how to handle the case when the intersection has the wrong" codimension. The intersection number is given by Serre's formula, and we give an example to show why the obvious simple formula for it fails. We discuss Chow's moving lemma, and give an example to show that even if we start with a positive cycle we might have to deform it to a non-positive one. Finally we mention a few cases when we can calculate the Chow ring.