2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104722S. Kondō defined a birational period map from the moduli space of genus three curves to a moduli space of degree four polarized K3 surfaces. In this paper we extend the period map to a surjective morphism on a suitable compactification of $\mathcal M_3$ and describe its geometry.Algebraic Geometry14J10, 14J28, 14H10text