1 citations · 1 across the 4 of their papers we have counts for
8 papers
Venereau polynomials and related fiber bundles
Shulim Kaliman, Mikhail Zaidenberg
The Venereau polynomials v-n:=y+x^n(xz+y(yu+z^2)), n>= 1, on A4 have all fibers isomorphic to the affine space A3. Moreover, for all n>= 1 the map (v-n, x) : A4 -> A2 yields a flat…
-actions on contractible threefolds
Shulim Kaliman, Nikolai Saveliev
Let be a smooth contractible affine algebraic threefold with a nontrivial algebraic -action on it. We show that is rational and the algebraic quotient $X//{\bf C…
Subrings invariant under endomorphisms
Shulim Kaliman
Let S and R be the rings of regular functions on affine algebraic varieties over a field of characteristic 0, R be embedded as a subring in S, and F : S --> S be an endomorphism su…
Free C_+ -actions on C^3 are translations
Shulim Kaliman
Let X' be a smooth contractible three-dimensional affine algebraic variety with a free algebraic C_+ -action on it such that S =X'// C_+ is smooth. We prove that X' is isomorphic t…
Simple birational extensions of the polynomial ring $\C^{[3]}$
Sh. Kaliman, St. Venereau, M. Zaidenberg
The Abhyankar-Sathaye Problem asks whether any biregular embedding of affine spaces can be rectified, that is, is equivalent to a linear embedding up to an automor…
Polynomials with general C^2-fibers are variables. I
Shulim Kaliman
Suppose that X' is a smooth affine algebraic variety of dimension 3 with H_3(X')=0 which is a UFD and whose invertible functions are constants. Suppose that Z is a Zariski open sub…