I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2009, VOLUME 15, NUMBER 1, PAGES 125-133
Varieties birationally isomorphic to affine
A. V. Petukhov
View as HTML
View as gif image
Let a linear algebraic group act on an algebraic
Classification of all these actions, in particular birational
classification, is of great interest.
A complete classification related to Galois cohomologies of the
Another important question is reducibility, in some sense, of this
action to an action of on an affine variety.
It has been shown that if the stabilizer of a typical point under
the action of a reductive group on
a variety is reductive, then
birationally isomorphic to an affine variety with stable
action of .
In this paper, I show that if a typical orbit of the action
quasiaffine, then the variety is birationally
isomorphic to an affine variety .
Last modified: December 2, 2009