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The moduli stack of affine stable toric varieties
Olga V. Chuvashova, Nikolay A. Pechenkin
Let X be an irreducible affine T-variety. We consider families of affine stable toric T-varieties over X and give a description of the corresponding moduli space as the quotient st…
Quotients of an affine variety by an action of a torus
Olga V. Chuvashova, Nikolay A. Pechenkin
Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/_CT and the toric Hilbert scheme H. We introduce a notion of the…
The main component of the toric Hilbert scheme
O. V. Chuvashova
Let \X be an affine toric variety under a torus \T and let T be a subtorus. The general T-orbit closures in \X and their flat limits are parametrized by the main component H_0 of t…
The separation properties for closures of toric orbits
Olga V. Chuvashova
A subset X of a vector space V is said to have the "Separation Property" if it separates linear forms in the following sense: given a pair (a, b) of linearly independent forms on V…
Classification of affine homogeneous spaces of complexity one
Ivan V. Arzhantsev, Olga V. Chuvashova
The complexity of an action of a reductive algebraic group G on an algebraic variety X is the codimension of a generic B-orbit in X, where B is a Borel subgroup of G. We classify a…