96 research outputs found
Subrings invariant under endomorphisms
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 such that F(R) subset R. Suppose that every ideal of
height 1 in R generates a proper ideal in S, and the spectrum of R has no
selfintersection points. We show that if F is an automorphism so is F|_R : R
--> R. When R and S have the same transcendence degree then the fact that F|_R
is an automorphisms implies that F is an automorphism.Comment: 16 page
One more proof of the Abhyankar-Moh-Suzuki theorem
We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.Comment: 4 page
On the present state of the Andersen-Lempert theory
In this survey of the Andersen-Lempert theory we present the state of the art
in the study of the density property (which means that the Lie algebra
generated by completely integrable holomorphic vector fields on a given Stein
manifold is dense in the space of all holomorphic vector fields). There are
also two new results in the paper one of which is the theorem stating that the
product of Stein manifolds with the volume density property possesses such a
property as well. The second one is a meaningful example of an algebraic
surface without the algebraic density property. The proof of the last fact
requires Brunella's technique.Comment: 40 page
- …