CONJECTURE OF TITS TYPE FOR COMPLEX VARIETIES AND THEOREM OF LIE-KOLCHIN TYPE FOR A CONE

摘要

First, we formulate and prove Theorem of Lie-Kolchin type for a cone and derive some algebro-geometric consequences. Next, inspired by a recent result of Dinh and Sibony we pose a conjecture of Tits type for a group of automorphisms of a complex variety and verify its weaker version. Finally, applying Theorem of Lie-Kolchin type for a cone, we confirm the conjecture of Tits type for complex tori, hyperk_hler manifolds, surfaces, and minimal threefolds.