Chern classes of free hypersurface arrangements

TL;DR

This paper extends the known equality between the Chern class of the sheaf of logarithmic derivations and the Chern-Schwartz-MacPherson class from simple normal crossing divisors to more general free hyperplane arrangements, broadening the understanding of characteristic classes in algebraic geometry.

Contribution

It generalizes the equality of Chern classes to divisors locally isomorphic to free hyperplane arrangements, beyond simple normal crossing cases.

Findings

Equality holds for more general free hyperplane arrangements

Extends known results to broader classes of divisors

Provides new tools for studying characteristic classes in algebraic geometry

Abstract

The Chern class of the sheaf of logarithmic derivations along a simple normal crossing divisor equals the Chern-Schwartz-MacPherson class of the complement of the divisor. We extend this equality to more general divisors, which are locally analytically isomorphic to free hyperplane arrangements.