15 citations · 86 across the 13 of their papers we have counts for
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Root subgroups on affine spherical varieties
Ivan Arzhantsev, Roman Avdeev
Given a connected reductive algebraic group and a Borel subgroup , we study -normalized one-parameter additive group actions on affine spherical -varieties…
Degenerations of spherical subalgebras and spherical roots
Roman Avdeev
We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgrou…
Spherical actions on isotropic flag varieties and related branching rules
Roman Avdeev, Alexey Petukhov
Let be a symplectic or special orthogonal group, let be a connected reductive subgroup of , and let be a flag variety of . We classify all triples such…
New and old results on spherical varieties via moduli theory
Roman Avdeev, Stéphanie Cupit-Foutou
Given a connected reductive algebraic group and a finitely generated monoid of dominant weights of , in 2005 Alexeev and Brion constructed a moduli scheme …
On the irreducible components of moduli schemes for affine spherical varieties
Roman Avdeev, Stéphanie Cupit-Foutou
We give a combinatorial description of all affine spherical varieties with prescribed weight monoid . As an application, we obtain a characterization of the irreducible componen…
Strongly solvable spherical subgroups and their combinatorial invariants
Roman Avdeev
A subgroup H of an algebraic group G is said to be strongly solvable if H is contained in a Borel subgroup of G. This paper is devoted to establishing relationships between the fol…
Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup
Roman Avdeev
For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgro…
An epimorphic subgroup arising from Roberts' counterexample
Roman Avdeev
In 1994, based on Roberts' counterexample to Hilbert's fourteenth problem, A'Campo-Neuen constructed an example of a linear action of a 12-dimensional commutative unipotent group H…