Subvarieties of C^n with non-extendible Automorphisms
We investigate algebraic and analytic subvarieties of C^n with automorphisms which can not be extended to the ambient space.
math.AG↗
arXiv subjects
Joerg Winkelmann
Publications and source records attributed to Joerg Winkelmann.
Holomorphic functions on an algebraic group invariant under a Zariski-dense subgroup
Let G be complex linear-algebraic group, H a subgroup, which is dense in G in the Zariski-topology. Assume that G/[G,G] is reductive and furthermore that (1) G is solvable, or (2) the semisimple elements in G'=[G,G] are dense. Then every H-invariant holomorphic function on G is constant. If G=G', furthermore every H-invariant meromorphic or plurisubharmonic function is constant. Finally an example of Margulis is used to show the existence of an algebraic group G with G=G' such that there exists a Zariski-dense discrete subgroup without any semisimple element.
alg-geom↗