Existence of Invariant Planes in a Complex Projective 3-Space under Discrete Projective Transformation Groups

摘要

Let Γ be a finitely generated discrete subgroup of PGL(4, C) acting on P~3. Suppose that Γ leaves invariant a surface in P~3. Then, except for a few cases, we can find a plane which is invariant by a finite index subgroup of Γ. The exceptional cases will be determined explicitly.