Flag varieties, toric varieties, and suspensions: three instances of infinite transitivity

Details Flag varieties, toric varieties, and suspensions: three instances of infinite transitivity Flag varieties, toric varieties, and suspensions: three instances of infinite transitivity

2010-03-16

arxiv.org/abs/1003.3164v1

Mathematics

Algebraic Geometry

25 pages

Scientific paper

We say that a group G acts infinitely transitively on a set X if for every integer m the induced diagonal action of G is transitive on the cartesian mth power of X with the diagonals removed. We describe three classes of affine algebraic varieties such that their automorphism groups act infinitely transitively on their smooth loci. The first class consists of affine cones over flag varieties, the second of non-degenerate affine toric varieties, and the third of iterated suspensions over affine varieties with infinitely transitive automorphism groups of a reinforced type.

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