2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65483Naruki gave an explicit construction of the moduli space of marked cubic surfaces, starting from a toric variety and proceeding with blow ups and contractions. Using his result, we compute the Chow groups and the Chern classes of this moduli space.As an application we relate a recent result of Freitag on the Hilbert polynomial of a certain ring of modular forms to the Riemann-Roch theorem for the moduli space.23 pages, LaTeXAlgebraic Geometrytext