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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…
math.AG2023
Root subgroups on horospherical varieties
Roman Avdeev, Vladimir Zhgoon
Given a connected reductive algebraic group and a spherical -variety , a -root subgroup on is a one-parameter additive group of automorphisms of normalized by…