Journal of the Mathematical Society of Japan

Chern classes of logarithmic derivations for free divisors with Jacobian ideal of linear type


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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].

Article information

J. Math. Soc. Japan, Volume 70, Number 3 (2018), 975-988.

Received: 5 December 2016
First available in Project Euclid: 31 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
Secondary: 14J17: Singularities [See also 14B05, 14E15]

Chern–Schwartz–MacPherson class logarithmic derivation Jacobian ideal of linear type


LIAO, Xia. Chern classes of logarithmic derivations for free divisors with Jacobian ideal of linear type. J. Math. Soc. Japan 70 (2018), no. 3, 975--988. doi:10.2969/jmsj/76797679.

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