2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69433We prove that the Poincare' polynomial of the moduli space of smooth genus 4 curves is 1+t^2+t^4+t^5. We show this by producing a stratification of the space, such that all strata are geometric quotients of complements of discriminants.26 pagesAlgebraic GeometryAlgebraic Topology14H10 (Primary); 55R80, 14R30, 14F99 (Secondary)text