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- Ivan Arzhantsev
- 2007

We consider actions of reductive groups on a varieties with finitely generated Cox ring, e.g., the classical case of a diagonal action on a product of projective spaces. Given such an action, weâ€¦ (More)

We study equivariant embeddings with small boundary of a given homogeneous space G/H, where G is a connected, simply connected linear algebraic group with only trivial characters, and H âŠ‚ G is anâ€¦ (More)

- Ivan Arzhantsev, K. KUYUMZHIYAN, Mikhail Zaidenberg
- 2010

We say that a group G acts infinitely transitively on a set X if for every m âˆˆ N the induced diagonal action of G is transitive on the cartesian mth power X m \ âˆ† with the diagonals removed. Weâ€¦ (More)

We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings ofâ€¦ (More)

- Ivan Arzhantsev
- 2005

Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneousâ€¦ (More)

- Ivan Arzhantsev, Alexander Perepechko, Hendrik SÃ¼ÃŸ
- J. London Math. Society
- 2014

Let X be an algebraic variety covered by open charts isomorphic to the affine space and q : X â†’ X be the universal torsor over X. We prove that the automorphism group of the quasiaffine variety Xâ€¦ (More)

- Ivan Arzhantsev
- 2005

Let G be a reductive algebraic group and H a closed subgroup of G. Explicit constructions of G-invariant ideals in the algebra K[G/H] are given. This allows to obtain an elementary proof ofâ€¦ (More)

- Ivan Arzhantsev
- 2008

Generalized Coxâ€™s construction associates with an algebraic variety a remarkable invariant â€“ its total coordinate ring, or Cox ring. In this note we give a new proof of factoriality of the Cox ringâ€¦ (More)

- Ivan Arzhantsev
- 2006

New and old results on closed polynomials, i.e., such poly-nomials f âˆˆ k[x1,. .. , xn] \ k that the subalgebra k[f ] is integrally closed in k[x1,. .. , xn], are collected in the paper. Using someâ€¦ (More)

- Ivan Arzhantsev, ANATOLIY P. PETRAVCHUK
- 2007

New and old results on closed polynomials, i.e., such poly-nomials f âˆˆ k[x1,. .. , xn] \ k that the subalgebra k[f ] is integrally closed in k[x1,. .. , xn], are collected in the paper. Using someâ€¦ (More)