Roman Avdeev

collaborators

4 papers

math.AC2026

An infinite series of Gorenstein local algebras failing the affine homogeneity property

Roman Avdeev, Yulia Zaitseva

We provide an infinite series of commutative finite-dimensional Gorenstein local algebras $A_{n}$ for $n \geq 2$ . We give an elementary proof that the maximal ideal of every algebra $…

math.AG2026

Connecting orbits in quasiaffine spherical varieties via $B$ -root subgroups

Roman Avdeev, Vladimir Zhgoon

Given a connected reductive algebraic group $G$ with a Borel subgroup $B$ and a quasiaffine spherical $G$ -variety $X$ , we prove that every $G$ -orbit $Y$ contained in the regular lo…

math.AG2026

Algebraic monoid structures on the affine 3-space

Ivan Arzhantsev, Roman Avdeev, Yulia Zaitseva

We complete the classification of algebraic monoid structures on the affine 3-space. The result is based on a reduction of the general case to that of commutative monoids. We also…

math.AG2024

Root subgroups on horospherical varieties