(Volume) density property of a family of complex manifolds including the Koras-Russell cubic threefold

Leuenberger, Matthias (2016). (Volume) density property of a family of complex manifolds including the Koras-Russell cubic threefold. Proceedings of the American Mathematical Society, 144(9), pp. 3887-3902. American Mathematical Society 10.1090/proc/13030

[img]
Preview
Text
leuenberger1.pdf - Accepted Version
Available under License Publisher holds Copyright.

Download (218kB) | Preview

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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Leuenberger, Matthias

Subjects:

500 Science > 510 Mathematics

ISSN:

0002-9939

Publisher:

American Mathematical Society

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

12 Jul 2017 10:56

Last Modified:

12 Jul 2017 10:56

Publisher DOI:

10.1090/proc/13030

ArXiv ID:

1507.03842v1

BORIS DOI:

10.7892/boris.98615

URI:

https://boris.unibe.ch/id/eprint/98615

Actions (login required)

Edit item Edit item
Provide Feedback