arXiv subjects

Ilya Boldyrev

Publications and source records attributed to Ilya Boldyrev.

3 recordsLinked to original sources

arXiv2024

Modified Derksen invariant

Modified Derksen invariant HD*(X) of an affine variety X is a subalgebra in K[X] generated by kernels of all locally nilpotent derivations of K[X] with slices. If there is a locally nilpotent derivation of K[X] with a slice then X is a product of Y and a line, where Y is an affine variety. We prove that there are three possibilities: A) HD*(X) = K[X]; B) HD*(X) is a proper infintely generated subalgebra; C) HD*(X) = \BK[Y]. We give examples for each case, and also provide sufficient conditions for the variety Y so that the variety X belongs to one of the type.

math.AG↗

arXiv2022

Makar-Limanov invariants of nonnormal affine toric varieties

We prove the equality of the Makar-Limanov invariant and the modified Makar-Limanov invariant in the case of not necessary normal affine toric varieties. Also we give a combinatorial description of these invariants.

math.AG↗

arXiv2020

Automorphisms of nonnormal toric varieties

In this paper we prove criteria for a nonnormal toric variety to be flexible, to be rigid and to be almost rigid. For rigid and almost rigid toric varieties we describe the automorphism group explicitly.

math.AG↗