2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156281In this note we survey Hodge-theoretic formulae of Atiyah-Meyer type for genera and characteristic classes of complex algebraic varieties, and derive some new and interesting applications. We also present various extensions to the singular setting of the Chern-Hirzebruch-Serre signature formula.Revised version to be published in the Proceedings of the School and Workshop on the Geometry and Topology of Singularities (L^e Fest). Few typos corrected and some cosmetic changesAlgebraic GeometryAlgebraic Topology57R20, 32S20, 14C30, 32S35, 14D07, 55N33text