2 citations · 3 across the 5 of their papers we have counts for
6 papers
Toric varieties admitting an action of a unipotent group with a finite number of orbits
Anton Shafarevich
We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where…
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…
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.…
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…