3 citations · 5 across the 5 of their papers we have counts for
9 papers
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…
Closed and Irreducible Polynomials in Several Variables
Ivan V. Arzhantsev, Anatoliy P. Petravchuk
New and old results on closed polynomials, i.e., such polynomials f in K[x_1,...,x_n] that the subalgebra K[f] is integrally closed in K[x_1,...,x_n], are collected. Using some pro…
On the multiplication map of a multigraded algebra
Ivan V. Arzhantsev, Juergen Hausen
Given a multigraded algebra , it is a natural question whether or not for two homogeneous components and , the product is the whole component $A_{nu+nv…
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…