Chern classes II: axiomatics

Dmitri Panov.

In this lecture we first cover a range of examples, such as a calculation of the number $27$ of lines on a cubic surface in $\mathbb CP^3$, and a calculation of Chern classes of the tangent bundle of $\mathbb CP^n$. The latter is an important calculation that can be used, for example, to find the Euler characteristic of a hypersurface of any degree. Finally we give an abstract definition of Chern classes, and show that they exist by exhibiting a construction a la Grothendieck.

There are some notes from previous years.