3 citations · 5 across the 5 of their papers we have counts for
7 papers · 1 filter
On factoriality of Cox rings
Ivan V. Arzhantsev
Generalized Cox's construction associates with an algebraic variety a remarkable invariant -- its total coordinate ring, or Cox ring. In this note we give a new proof of factoriali…
Geometric Invariant Theory via Cox Rings
Ivan V. Arzhantsev, Juergen Hausen
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…
On embeddings of homogeneous spaces with small boundary
Ivan V. Arzhantsev, Juergen Hausen
We study equivariant embeddings with small boundary of a given homogeneous space , where is a connected, linear algebraic group with trivial Picard group and only trivial…
Invariant Ideals and Matsushima's Criterion
Ivan V. Arzhantsev
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…
Affine embeddings of homogeneous spaces
Ivan V. Arzhantsev
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. W…
On affinely closed homogeneous spaces
Ivan V. Arzhantsev, Natalia A. Tennova
Affinely closed homogeneous spaces G/H, i.e., affine homogeneous spaces that admit only the trivial affine embedding, are characterized for any affine algebraic group G. As a corol…