Journal of the Mathematical Society of Japan

Chern number formula for ramified coverings

Takeshi IZAWA

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Abstract

For a ramified covering $f$ : $Y\rightarrow X$ between compact complex manifolds, we establish a formula relating the Chern numbers of $Y$ and $X$. We obtain the formula by localizing characteristic classes via the Čech-de Rham cohomology theory. As corollaries, we deduce generalizations of such formulas as the Riemann-Hurwitz formula and a formula of Hirzebruch for the signature, as well as formulas, for other invariants such as the Todd genus.

Article information

Source
J. Math. Soc. Japan Volume 52, Number 1 (2000), 1-15.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1213107651

Digital Object Identifier
doi:10.2969/jmsj/05210001

Mathematical Reviews number (MathSciNet)
MR1727204

Zentralblatt MATH identifier
0944.57022

Subjects
Primary: 57R20: Characteristic classes and numbers
Secondary: 32J25: Transcendental methods of algebraic geometry [See also 14C30]

Keywords
Characteristic classses ramified coverings

Citation

IZAWA, Takeshi. Chern number formula for ramified coverings. J. Math. Soc. Japan 52 (2000), no. 1, 1--15. doi:10.2969/jmsj/05210001. http://projecteuclid.org/euclid.jmsj/1213107651.


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