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math.AG2026
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…
math.AG2026
On Picard Number and Dimension of Algebraic Homogeneous Spaces
Ivan Beldiev, Dmitry Timashev
An algebraic variety is called a homogeneous space if there exists a transitive regular action of an algebraic group on . We prove inequalities between the dimension of a ho…
math.AG2025
The Lie algebra of polynomial vector fields on the affine space is -generated
Ivan Beldiev
We prove that the infinite-dimensional Lie algebra of polynomial vector fields on the affine space $\KK^n$ is generated by two explicitly given elements.