2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158423This article is a survey of P. Katsylo's proof that the moduli space of smooth projective complex curves of genus 3 is rational. We hope to make the argument more comprehensible and transparent by emphasizing the underlying geometry in the proof and its key structural features.39 pagesAlgebraic Geometry14E08; 14M20; 14L24text