Relatively minimal quasihomogeneous projective 3-folds

Abstract

In the present work we classify the relatively minimal 3-dimensional quasihomogeneous complex projective varieties under the assumption that the automorphism group is not solvable. By relatively minimal we understand varieties $X$ having at most $\mathbb{Q}$-factorial terminal singularities and allowing an extremal contraction $X \to Y$ where $\dim \, Y < 3$.