159 citations · 323 across the 40 of their papers we have counts for
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Algebraic ellipticity of quartic double spaces
Alexander Dvorsky, Shulim Kaliman, Mikhail Zaidenberg
We prove that every smooth quartic double -fold, , over an algebraically closed field of characteristic zero is algebraically elliptic in Gromov's sense. In particular, e…
A remark on Banecki's theorem
Shulim Kaliman
J. Banecki proved that every smooth projective rational variety is algebraically elliptic in the sense of Gromov. Modifying his proof we show that the same is true for every smooth…
Gromov's ellipticity of principal -bundles
Shulim Kaliman
We prove that every nontrivial principal -bundle over a complete uniformly rational variety is algebraically elliptic in the sense of Gromov.
Algebraic Gromov's ellipticity of cubic hypersurfaces
Shulim Kaliman, Mikhail Zaidenberg
We show that every smooth cubic hypersurface X in P^{n+1}, n> 1 is algebraically elliptic in Gromov's sense. This gives the first examples of non-rational projective manifolds elli…
Varieties covered by affine spaces, uniformly rational varieties and their cones
I. Arzhantsev, S. Kaliman, M. Zaidenberg
It was shown in [S. Kaliman, M. Zaidenberg, Gromov ellipticity of cones over projective manifolds, Math. Res. Lett. (to appear), arXiv:2303.02036 (2023)] that the affine cones over…
Gromov ellipticity of cones over projective manifolds
Shulim Kaliman, Mikhail Zaidenberg
We find classes of projective manifolds that are elliptic in the sense of Gromov and such that the affine cones over these manifolds also are elliptic off their vertices. For examp…
Gromov Ellipticity and subellipticity
Shulim Kaliman, Mikhail Zaidenberg
We establish the equivalence of Gromov ellipticity and subellipticity in the algebraic category.
Embedding theorem for flexible varieties
Shulim Kaliman
Let be an affine algebraic variety and be a smooth flexible variety. We develop some criteria under which admits a closed embedding into . In particular, we show tha…
Holme type theorem for special linear groups
Shulim Kaliman
Let Z be an affine algebraic variety and ED(Z)= max(2 dim Z+1, dim TZ). Let X be a smooth algebraic variety isomorphic to a semi-simple linear algebraic group whose Lie algebra is…
Lines in affine simlicial toric varieties
Shulim Kaliman
We prove that up to automorphisms a line admits a unique embedding into the regular part of of a simplicial toric variety of dimension n>=4 over an algebraically closed field of ch…
On automorphisms of flexible varieties
Shulim Kaliman, David Udumyan
Let X be a flexible variety of F be an isomorphism of closed one-dimensional subschemes of . We develop criteria which guarantee that F extends to au automorphism of X.
The Kraft-Russell Generic Equivalence Theorem and its application
Shulim Kaliman
We find some extensions of the Kraft-Russell Generic Equivalence Theorem and using it we obtain a simple proof of a result of Dubouloz and Kishimoto.
Cancellation for surfaces revisited. II
Hubert Flenner, Shulim Kaliman, Mikhail Zaidenberg
Let and be affine algebraic varieties over a field . The celebrated Zariski Cancellation Problem asks as to when the existence of an isomorphism $X\times\mathb…
Extensions of isomorphisms of subvarieties in flexile varieties
Shulim Kaliman
Let be a quasi-affine algebraic variety isomorphic to the complement of a closed subvariety of dimension at most in $\C^n$. We find some conditions under which an isomorp…
On subelliptic manifolds
Shulim Kaliman, Frank Kutzschebauch, Tuyen Trung Truong
A smooth complex quasi-affine algebraic variety is flexible if its special group $\SAut (Y)$ of automorphisms (generated by the elements of one-dimensional unipotent subgroups…
Cancellation for surfaces revisited. I
Hubert Flenner, Shulim Kaliman, Mikhail Zaidenberg
The celebrated Zariski Cancellation Problem asks as to when the existence of an isomorphism for (affine) algebraic varieties and…
One more proof of the Abhyankar-Moh-Suzuki theorem
Shulim Kaliman
We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.
Proper -actions on $\C^4$ preserving a coordinate
Shulim Kaliman
We prove that the actions mentioned in the title are translations. We show also that for certain -actions on affine fourfolds the quotient of the action is automatically affin…
Analytic extensions of algebraic isomorphisms
Shulim Kaliman
Let be an isomorphism of closed affine algebraic subvarities of $\C^n$ such that . We prove that can be extended to a holomorp…
The Gromov-Winkelmann theorem for flexible varieties
Hubert Flenner, Shulim Kaliman, Mikhail Zaidenberg
An affine variety of dimension is called {\em flexible} if its special automorphism group SAut acts transitively on the smooth locus \cite{AKZ}. Recall t…
Deformation equivalence of affine ruled surfaces
Hubert Flenner, Shulim Kaliman, Mikhail Zaidenberg
A smooth family of surfaces will be called {\em completable} if there is a logarithmic deformation over so that ${\mathca…
Infinite transitivity on affine varieties
I. Arzhantsev, H. Flenner, S. Kaliman +2
In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and exam…
On algebraic volume density property
Shulim Kaliman, Frank Kutzschebauch
A smooth affine algebraic variety equipped with an algebraic volume form has the algebraic volume density property (AVDP) if the Lie algebra generated by completely integra…
Flexible varieties and automorphism groups
I. Arzhantsev, H. Flenner, S. Kaliman +2
Given an affine algebraic variety X of dimension at least 2, we let SAut (X) denote the special automorphism group of X i.e., the subgroup of the full automorphism group Aut (X) ge…