159 citations · 404 across the 61 of their papers we have counts for
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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…
Infinite transitivity and polynomial vector fields
Rafael B. Andrist, Ivan Arzhantsev
We prove that for many pairs of root subgroups of the automorphism group the diagonal action of the group generated by on $(\mathbb…
Borel subalgebras of Lie algebras of vector fields
Ivan Arzhantsev, Mikhail Zaidenberg
In [I. Arzhantsev and M. Zaidenberg, Borel subgroups of the automorphism groups of affine toric surfaces, arXiv:2507.09679 (2025)] we described the Borel subgroups and maximal solv…
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…
Borel subgroups of the automorphism groups of affine toric surfaces
Ivan Arzhantsev, Mikhail Zaidenberg
In [I. Arzhantsev and M. Zaidenberg, Acyclic curves and group actions on affine toric surfaces. Affine Algebraic Geometry, 1--41. World Scientific Publishing Co. 2013] we described…
Algebraic monoid structures on the affine 3-space
Ivan Arzhantsev, Roman Avdeev, Yulia Zaitseva
We complete the classification of algebraic monoid structures on the affine 3-space. The result is based on a reduction of the general case to that of commutative monoids. We also…