3 citations · 8 across the 7 of their papers we have counts for
7 papers
Automorphisms of toric varieties and Gale duality
Ivan Arzhantsev, Kirill Shakhmatov
We classify complete toric threefolds such that the automorphism group acts on with an open orbit whose complement does not contain a divisor. The latter co…
Cylinders and the zero locus of the plinth ideal
Kirill Shakhmatov
Given a -action on an affine variety , we show that the complement of the union of all principal invariant cylinders in is equal to the zero locus of…
On flexibility of affine factorial varieties
Ivan Arzhantsev, Kirill Shakhmatov
We give a criterion of factoriality of a suspension. This allows to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine fact…
Radiant toric varieties and unipotent group actions
Ivan Arzhantsev, Alexander Perepechko, Kirill Shakhmatov
We consider complete toric varieties such that a maximal unipotent subgroup of the automorphism group acts on with an open orbit. It turns out that such…
Homogeneous algebraic varieties and transitivity degree
Ivan Arzhantsev, Kirill Shakhmatov, Yulia Zaitseva
Let be an algebraic variety such that the group acts on transitively. We define the transitivity degree of as a maximal number such that the action…
Some finiteness results on triangular automorphisms
Ivan Arzhantsev, Kirill Shakhmatov
In this note we prove that every finite collection of connected algebraic subgroups of the group of triangular automorphisms of the affine space generates a connected solvable alge…
Smooth non-projective equivariant completions of affine spaces
Kirill Shakhmatov
In this paper we construct an equivariant embedding of the affine space with the translation group action into a complete non-projective algebraic variety for al…