Chow ring 2: Chern classes
Channel: Richard E Borcherds
Date: 2020-12-03

This lecture give an overview of Chern classes of nonsingular algebraic varieties. We first define the Chern class of a lline bundle by looking at the cycle of zeros of a section. Then we define Chern classes of higher rank vector bundles by looking at the line bundle O(1) over the corresponding projective bundle. 

We finish by sketching how Chern classes are used in the Hirzebruch-Riemann-Roch and Grothendieck-Riemann-Roch theorems.