From the 1 of 6 linked papers with an AI index.
6 papers
Open surfaces with a triangle at infinity
Dmitriy Chunaev, Alexander Perepechko, Daniil Shunin
The paper classifies open algebraic surfaces whose compactifications contain a triangle of contractible (‑1)-curves, shows these affine surfaces coincide with cubic surfaces of Mar…
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…
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…
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…
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…
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…