Submission: 2014, Jan 1
We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results obtained are given.
2010 Mathematics Subject Classification: 14L30
Keywords and Phrases: automorphism group of algebraic variety, exhaustive algebraic family, orbit, invariant rational function, quotient
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