Quasihomogeneous $(C^{\ast }{)}^k\times S{L}_2(C)$-varieties containing a finite number of orbits

Abstract

Let $G:=(C^{\ast }{)}^k\times S{L}_2(C)$ act linearly on a vector space or its projectivisation. We obtain an effective criterion to detect whether a number of orbits in an orbit-closure is finite or not.

8 pages with 1 figure