Segre classes and invariants of singular varieties

TL;DR

This paper surveys how Segre classes are used to define and analyze invariants and characteristic classes of singular algebraic varieties, highlighting their importance in intersection theory.

Contribution

It provides a comprehensive overview of applications of Segre classes to invariants of singular spaces, including numerical invariants and characteristic classes.

Findings

Segre classes encode key intersection-theoretic information.

Applications include defining invariants and characteristic classes for singular varieties.

The paper reviews background in algebraic geometry and intersection theory.

Abstract

Segre classes encode essential intersection-theoretic information concerning vector bundles and embeddings of schemes. In this paper we survey a range of applications of Segre classes to the definition and study of invariants of singular spaces. We will focus on several numerical invariants, on different notions of characteristic classes for singular varieties, and on classes of Le cycles. We precede the main discussion with a review of relevant background notions in algebraic geometry and intersection theory.