A Backward Look from the Viewpoint of Characteristic Classes
The introduction of characteristic classes allows one to see many calculations carried out above in a new light and simplify them. Characteristic classes are a universal tool for computing topological characteristics of algebraic varieties, both smooth and singular. We begin with discussing definitions and general properties of Chern classes of vector bundles, and then show how one can use them to obtain some results we already know and their generalizations. In the next chapter, we will speak about characteristic classes that arise naturally in the study of the topology of moduli spaces of curves.