Conjecture of Tits type for complex varieties and Theorem of Lie-Kolchin type for a cone

Abstract

First, we shall 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 shall confirm the conjecture of Tits type for complex tori, hyperkähler manifolds, surfaces, and minimal threefolds.

16 pages

References in corpus (1)

• Tits alternative in hypekähler manifolds

Cited by in corpus (3)

• Super-potentials for currents on compact Kaehler manifolds and dynamics of automorphisms
• Automorphism groups and anti-pluricanonical curves
• Solvable automorphism groups of a compact Kaehler manifold