Mathematical Research Letters

Volume 16 (2009)

Number 1

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

Pages: 133 – 148

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n1.a13

Authors

JongHae Keum (Korea Institute for Advanced Study)

Keiji Oguiso (Korea Institute for Advanced Study)

De-Qi Zhang (National University of Singapore)

Abstract

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, hyperkähler manifolds, surfaces, and minimal threefolds.

Full Text (PDF format)