159 citations · 404 across the 61 of their papers we have counts for
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Cox rings, semigroups and automorphisms of affine algebraic varieties
Ivan V. Arzhantsev, Sergey A. Gaifullin
We study the Cox realization of an affine variety, i.e., a canonical representation of a normal affine variety with finitely generated divisor class group as a quotient of a factor…
Saturated subfields and invariants of finite groups
Ivan V. Arzhantsev, Anatoliy P. Petravchuk
Every subfield $\kk(ϕ)$ of the field of rational functions $\kk(x_1,...,x_n)$ is contained in a unique maximal subfield of the form $\kk(ψ)$. The element is called generative f…
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…
Projective embeddings of homogeneous spaces with small boundary
Ivan V. Arzhantsev
We study open equivariant projective embeddings of homogeneous spaces such that the complement of the open orbit does not contain divisors. Criterions of existence of such an embed…