22 citations · 34 across the 14 of their papers we have counts for
16 papers
Non-cancellative varieties, maximal tori, and the Makar-Limanov invariant
Sergey Gaifullin, Mikhail Petrov
In this paper, we construct a wide class of new counterexamples to the generalized Zariski cancellation problem. The cylinders over these counterexamples have infinitely many non-c…
Flexibility criterion for affine horospherical varieties
Sergey Gaifullin, Veronika Kikteva
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal ho…
On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings
Ivan Arzhantsev, Sergey Gaifullin, Viktor Lopatkin
For a finite set of homogeneous locally nilpotent derivations of the algebra of polynomials in several variables, a finite dimensionality criterion for the Lie algebra generated by…
Modified Derksen invariant
Ilya Boldyrev, Sergey Gaifullin, Anton Shafarevich
Modified Derksen invariant HD*(X) of an affine variety X is a subalgebra in K[X] generated by kernels of all locally nilpotent derivations of K[X] with slices. If there is a locall…
Rigid Trinomial Varieties
Polina Evdokimova, Sergey Gaifullin, Anton Shafarevich
An algebraic variety is called rigid if there is no non-trivial action on of the additive group of the base field. A trinomial variety is an affine variety that is given by…
Modified Makar-Limanov and Derksen invariants
Sergey Gaifullin, Anton Shafarevich
We investigate modified Makar-Limanov and Derksen invariants of an affine algebraic variety. The modified Makar-Limanov invariant is the intersection of kernels of all locally nilp…
Automorphism group orbits on horospherical varieties and divisor class group
Sergey Gaifullin
In 2013 Bazhov proved a criterium for two points on a complete toric variety to lie in the same orbit of the neutral component of automorphism group. This criterium is in terms of…
Orbits of automorphism group of trinomial hypersurfaces
Sergey Gaifullin, Georgiy Shirinkin
Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the…
On orbits of automorphism groups on horospherical varieties
Viktoriia Borovik, Sergey Gaifullin, Anton Shafarevich
In this paper we describe orbits of automorphism group on a horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations.…
Automorphisms of nonnormal toric varieties
Ilya Boldyrev, Sergey Gaifullin
In this paper we prove criteria for a nonnormal toric variety to be flexible, to be rigid and to be almost rigid. For rigid and almost rigid toric varieties we describe the automor…
Isolated torus invariants and automorphism groups of rigid varieties
Viktoria Borovik, Sergey Gaifullin
Perepechko and Zaidenberg conjectured that the neutral component of the automorphism group of a rigid affine variety is a torus. We prove this conjecture for toric varieties and va…
On rigidity of trinomial hypersurfaces and factorial trinomial varieties
Sergey Gaifullin
Trinomial varieties are affine varieties given by some special system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal…
Flexibility of normal affine horospherical varieties
Sergey Gaifullin, Anton Shafarevich
We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a loca…
The automorphism group of a rigid affine variety
Ivan Arzhantsev, Sergey Gaifullin
An irreducible algebraic variety is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group of a…
Homogeneous toric varieties
Ivan V. Arzhantsev, Sergey A. Gaifullin
A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctur…
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…