2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228229By the technique of 3-fold Mori theory, we prove that the moduli space whose general point parameterizes a couple of a smooth curve of genus 4 and a halfcanonical divisor with vanishing global section is rational.This is our third paper. This paper is new and the results were obtained as applications of the first and second papersAlgebraic Geometry14H10, 14E30 (Primary) 14J45, 14N05, 14M20 (Secondary)text