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 $SL_2/\Gamma, \Gamma$ a finite subgroup, or that $X$ can be equivariantly transformed into $\Pthree$, the quadric $\QZ_3$, or into certain quasihomogeneous bundles with very simple structure.