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 [Alu12b].
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