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

Ivan Arzhantsev (1) , Karine Kuyumzhiyan (1, 2) , Mikhail Zaidenberg (2)

1 SMI | RAS - Steklov Mathematical Institute [Moscow]
2 IF - Institut Fourier

We say that a group G acts infinitely transitively on a set X if for every natural n, the induced diagonal action of G is transitive on the cartesian m-th 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.

, Volume 203, Number 7

Mots clés: Flag varieties; group actions; toric varieties; affine varieties; transitivity

Domaines: Géométrie algébrique [math.AG]

Ivan Arzhantsev, Karine Kuyumzhiyan, Mikhail Zaidenberg. Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity. Sbornik: Mathematics, 2012, 203 (7), pp.923-949. ⟨10.1070/SM2012v203n07ABEH004248⟩. ⟨hal-00463347⟩