Chern number formula for ramified coverings

Abstract

For a ramified covering $f$ : $Y\to X$ 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.