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

Xia Liao

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. Out result establishes a conjecture by Aluffi raised in [Alu12b].