2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60605We introduce orbifold Euler numbers for normal surfaces with Q-divisors. These numbers behave multiplicatively under finite maps and in the log canonical case we prove that they satisfy the Bogomolov-Miyaoka-Yau type inequality. As a corollary we prove effective versions of Bogomolov's result on boundedness of rational curves in some surfaces of general type. Finally, we give some applications to singularities of plane curves.37 pages; AMSTeXAlgebraic Geometry14J17; 14J29; 14C17text