Characteristic classes of mixed Hodge modules and applications

TL;DR

This paper reviews recent advances in characteristic class theories for singular spaces, focusing on the interaction with Saito's mixed Hodge modules, highlighting key applications in complex algebraic geometry.

Contribution

It provides an overview of the integration of characteristic classes with mixed Hodge modules, emphasizing new applications and theoretical developments.

Findings

Connection between characteristic classes and mixed Hodge modules clarified

New applications in complex algebraic geometry demonstrated

Framework for future research in singular space invariants established

Abstract

These notes are an extended version of the authors' lectures at the 2013 CMI Workshop "Mixed Hodge Modules and Their Applications". We give an overview, with an emphasis on applications, of recent developments on the interaction between characteristic class theories for singular spaces and Saito's theory of mixed Hodge modules in the complex algebraic context.