arXiv subjects
Publications and source records attributed to Polina Evdokimova.
We study multi Danielewski varieties, which are the generalization of Danielewski varieties and Double Danielewski varieties. The paper contains description of the Makar-Limanov invariant of these varieties and of their isomorphism classes.
We say that a locally nilpotent derivations $δ$ is maximal if there are no inequivalent locally nilpotent derivations that commute with $δ$. 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.
An algebraic variety $X$ is called rigid if there is no non-trivial action on $X$ of the additive group of the base field. A trinomial variety is an affine variety that is given by a set of equations consisting of polynomials with three monomials; see Definition 1. In this paper, we complete the classification of rigid trinomial varieties.