Simple models of quasihomogeneous projective 3-folds

Abstract

Let $X$ be a projective complex 3-fold, quasihomogeneous with respect to an action of a linear algebraic group. We show that $X$ is a compactification of $S{L}_2/\Gamma ,\Gamma$ a finite subgroup, or that $X$ can be equivariantly transformed into ${\mathbb{P}}_3$, the quadric ${\mathbb{Q}}_3$, or into certain quasihomogeneous bundles with very simple structure.