popovvl@orc.ru

Submission: 2010, Jan 8

A simple method of constructing a big stock of algebraic varieties with trivial Makar-Limanov invariant is described; the Derksen invariant of some varieties is computed; the generalizations of the Makar-Limanov and Derksen invariants are introduced and discussed; and some results on the Jordan property of automorphism groups of algebraic varieties are obtained.

2000 Mathematics Subject Classification: 14A10

Keywords and Phrases: the Makar-Limanov invariant, the Derksen invariant, group action, automorphism group, Jordan group

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