Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 70, Number 3 (2018), 975-988.
Chern classes of logarithmic derivations for free divisors with Jacobian ideal of linear type
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].
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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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