Journal of the Mathematical Society of Japan

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

Xia LIAO

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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].

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1527795358

Digital Object Identifier
doi:10.2969/jmsj/76797679

Mathematical Reviews number (MathSciNet)
MR3830794

Zentralblatt MATH identifier
06966969

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

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1527795358


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