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math.AG2026
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…
math.AG2026
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…
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…