2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225431In this paper, we study the period map of a certain one-parameter family of quartic K3 surfaces with an S5-action. We construct automorphic forms on the period domain as the pull-backs of theta constants of genus 2 by a modular embedding. Using these automorphic forms, we give an explicit presentation of the inverse period map.70 pages including an appendix by Tomohide TerasomaAlgebraic GeometryNumber Theory14J15; 14J28text