2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122260Let $X$ be a complex Calabi-Yau variety, that is, a complex projective variety with canonical singularities whose canonical class is numerically trivial. Let $G$ be a finite group acting on $X$ and consider the quotient variety $X/G$. The aim of this paper is to determine the place of $X/G$ in the birational classification of varieties. That is, we determine the Kodaira dimension of $X/G$ and decide when it is uniruled or rationally connected. If $G$ acts without fixed points, then $κ(X/G)=κ(X)=0$; thus the interesting case is when $G$ has fixed points. We answer the above questions in terms of the action of the stabilizer subgroups near the fixed points. We give a rough classification of possible stabilizer groups which cause $X/G$ to have Kodaira dimension $-\infty$ or equivalently (as we show) to be uniruled. These stabilizers are closely related to unitary reflection groups.Theorem 3 has been corrected. 27 pagesAlgebraic GeometryGroup Theory14J32, 14K05, 20E99 (Primary) 14M20, 14E05, 20F55 (Secondary)text