For a ramified covering : between compact complex manifolds, we establish a formula relating the Chern numbers of and . 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.
Takeshi IZAWA. "Chern number formula for ramified coverings." J. Math. Soc. Japan 52 (1) 1 - 15, January, 2000. https://doi.org/10.2969/jmsj/05210001