(Volume) density property of a family of complex manifolds including the Koras-Russell cubic threefold
Publisher DOI
Abstract
We present modified versions of existing criteria for the density property and the volume density property of complex manifolds. We apply these methods to show the (volume) density property for a family of manifolds given by x²y=a(z) + xb(z) with z =(z₀,...,zn) ⋲ Cn+¹ and holomorphic volume form dx/x²ʌdz₀ ʌ...ʌdzn. The key step is to show that in certain cases transitivity of the action of (volume preserving) holomorphic automorphisms implies the (volume) density property, and then to give sufficient conditions for the transitivity of this action. In particular, we show that the Koras-Russell cubic threefold {x²y + x + z2/0 + z3/1 =0} has the density property and the volume density property.
Date Issued
2016
Publication Type
Article
Subject(s)
Language(s)
en
Additional Credits
Journal
Proceedings of the American Mathematical Society
Publisher
American Mathematical Society
ISSN
0002-9939
Access(Rights)
open.access