Chern Classes of Logarithmic Derivations for Free Divisors with Jacobian Ideal of Linear Type

Abstract

Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$, and $D$ be a free divisor with Jacobian ideal of linear type. We compute the Chern class of the sheaf of logarithmic derivations along $D$ and compare it with the Chern-Schwartz-MacPherson class of the hypersurface complement. Our result establishes a conjecture by Aluffi raised in \cite{hyparr}.

To appear in the Journal of the Mathematical Society of Japan

References in corpus (3)

• A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors
• Chern Classes Of Logarithmic Vector Fields For Locally-Homogenous Free Divisors
• Chern Classes of Logarithmic Vector Fields

Cited by in corpus (1)

• Chern classes of logarithmic derivations for some non-free arrangements