Conjecture of tits type for complex variesties and theorem of Lie-Kolchin type for a cone

• Autores: JongHae Keum, Keiji Oguiso, De-Qui Zhang
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 16, Nº 1, 2009, págs. 133-148
• Idioma: inglés
• DOI: 10.4310/mrl.2009.v16.n1.a13
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• Resumen

  • 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\"ahler manifolds, surfaces, and minimal threefolds.