arXiv subjects
Publications and source records attributed to Dmitriy Chunaev.
A triangle surface is an open algebraic surface completed by a triangle of contractible $(-1)$-curves. We establish a combinatorial description of their completions. We also show that affine triangle surfaces are exactly cubic surfaces of Markov type. Explicit description of their automorphism groups is provided.
We say that a locally nilpotent derivations $\delta$ is maximal if there are no inequivalent locally nilpotent derivations that commute with $\delta$. The paper gives a description of isotropy groups of maximal homogeneous locally nilpotent derivations on affine toric varieties and on certain trinomial hypersurfaces. Moreover, the criteria for homogeneous locally nilpotent derivations to be maximal were obtained for these classes of varieties.
In this work we obtain sufficient conditions for a variety with a torus action of complexity one to have a finite number of automorphism group orbits.