2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79207We calculate the Hirzebruch $χ_y$ and $\hatχ_y$-genera of symmetric products of closed complex manifolds by the holomorphic Lefschetz formula of Atiyah and Singer \cite{Ati-Sin}. Such calculation rederive some formulas proved in an earlier paper \cite{Zho} by a different method.Differential Geometrytext