36 citations · 91 across the 17 of their papers we have counts for
18 papers · 1 filter
Neutral components of automorphism groups of (semi)rigid affine varieties
Alexander Perepechko
We say that an affine variety is (semi)rigid if all nontrivial actions of the additive group on have the same invariant ring. Then all such actions comprise the abelian sub…
Open surfaces with a triangle at infinity
Dmitriy Chunaev, Alexander Perepechko, Daniil Shunin
A triangle surface is an open algebraic surface completed by a triangle of contractible -curves. We establish a combinatorial description of their completions. We also show t…
Automorphism groups of non-normal rigid affine surfaces are finite-dimensional
Ivan Beldiev, Alexander Perepechko
It was recently established by Perepechko and Zaidenberg that the automorphism group of a normal affine surface is finite-dimensional if and only if the surface admits no non-trivi…
Additive actions on projective surfaces with a finite number of orbits
Alexander Perepechko
An additive action on an algebraic variety is an effective action of the vector group with an open orbit. We describe projective surfaces with du Val singularities that admit an ad…
Structure of connected nested automorphism groups
Alexander Perepechko
In this article, we describe the maximal unipotent subgroups of , where is an affine algebraic variety. Every subgroup of this type has a structure analogous t…
Generic flexibility of affine cones over del Pezzo surfaces in Sagemath
Alexander Perepechko
Generic flexibility of affine cones over Fano varieties is a subject of active study recently. For del Pezzo surfaces the question is completely studied in degree at least 3, and p…
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…
Automorphism groups of rigid affine surfaces: the identity component
Alexander Perepechko, Mikhail Zaidenberg
It is known that the identity component of the automorphism group of a projective algebraic variety is an algebraic group. This is not true in general for quasi-projective varietie…
Automorphism groups of affine varieties consisting of algebraic elements
Alexander Perepechko, Andriy Regeta
Given an affine algebraic variety , we prove that if the neutral component of the automorphism group consists of algebraic elements, then it is nested, i…
Affine cones over cubic surfaces are flexible in codimension one
Alexander Perepechko
Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codi…
When is the automorphism group of an affine variety nested?
Alexander Perepechko, Andriy Regeta
For an affine algebraic variety , we study the subgroup of the group of regular automorphisms of generated by all the connec…
Flexible affine cones and flexible coverings
Matheusz Michałek, Alexander Perepechko, Hendrik Süß
We provide a new criterion for flexibility of cones over varieties covered by flexible affine varieties. We apply this criterion to prove flexibility of affine cones over secant va…
On automorphism groups of affine surfaces
Sergei Kovalenko, Alexander Perepechko, Mikhail Zaidenberg
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these auto…
Demazure roots and spherical varieties: the example of horizontal SL(2)-actions
Kevin Langlois, Alexander Perepechko
Let be a connected reductive group, and let be an affine -spherical variety. We show that the classification of -actions on normalized by can be…
Infinite transitivity on universal torsors
Ivan Arzhantsev, Alexander Perepechko, Hendrik Süß
Let X be an algebraic variety covered by open charts isomorphic to the affine space and q: X' \to X be the universal torsor over X. We prove that the automorphism group of the quas…
Flexibility of affine cones over del Pezzo surfaces of degree 4 and 5
Alexander Perepechko
We prove that the action of the special automorphism group on affine cones over del Pezzo surfaces of degree 4 and 5 is infinitely transitive.
On solvability of the automorphism group of a finite-dimensional algebra
Alexander Perepechko
Consider an automorphism group of a finite-dimensional algebra. S. Halperin conjectured that the unity component of this group is solvable if the algebra is a complete intersection…
Affine algebraic monoids as endomorphisms' monoids of finite-dimensional algebras
Alexander Perepechko
In this note we prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.