3 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 for . We give an elementary proof that the maximal ideal of every algebra $…
math.AG2025
Connecting orbits in quasiaffine spherical varieties via -root subgroups
Roman Avdeev, Vladimir Zhgoon
Given a connected reductive algebraic group with a Borel subgroup and a quasiaffine spherical -variety , we prove that every -orbit contained in the regular lo…
math.AG2024
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…