This article is a survey on ind-varieties and ind-groups introduced by Shafarevich in 1965,
with a special emphasis on automorphism groups of affine varieties and actions of ind …

Let U be a graded unipotent group over the complex numbers, in the sense that it has an
extension U ̂ by the multiplicative group such that the action of the multiplicative group by …

In this article we review the question of constructing geometric quotients of actions of linear
algebraic groups on irreducible varieties over algebraically closed fields of characteristic …

We show that the automorphism group of affine $ n $-space ${\mathbb {A}^ n} $ determines
${\mathbb {A}^ n} $ up to isomorphism: If $ X $ is a connected affine variety such that …

We discuss various aspects of affine space fibrations f: X → Y f: X→ Y including the generic
fiber, singular fibers and the case with a unipotent group action on X. The generic fiber X_ η …

For certain actions of the Weyl groupoid $\mathfrak {W} $ from [Sergeev and Veselov,
Grothendieck rings of basic classical Lie superalgebras, Ann Math, 2011] on an affine …

We compute the finite generation ideal for Daigle and Freudenburg's counterexample to
Hilbert's fourteenth problem. This ideal helps to understand how far the ring of invariants is …

We show that any normal irreducible affine $ n $-dimensional $ SL_n $-variety $ X $ is
determined by its automorphism group in the category of normal irreducible affine varieties …

Let G be a linear algebraic group acting linearly on a vector space (or more generally, an
affine variety) V, and let k VG be the corresponding algebra of invariant polynomial …

A smooth $ d $-dimensional projective variety $ X $ can always be embedded into $2 d+ 1$-
dimensional space. In contrast, a singular variety may require an arbitrary large ambient …