Abstract
We introduce the notion of algebraic volume density property for affine algebraic manifolds and prove some important basic facts about it, in particular that it implies the volume density property. The main results of the paper are producing two big classes of examples of Stein manifolds with volume density property. One class consists of certain affine modifications of ℂn equipped with a canonical volume form, the other is the class of all Linear Algebraic Groups equipped with the left invariant volume form.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 605-647 |
| Number of pages | 43 |
| Journal | Inventiones Mathematicae |
| Volume | 181 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2010 |
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ASJC Scopus subject areas
- Mathematics(all)
Cite this
Algebraic volume density property of affine algebraic manifolds. / Kaliman, Shulim; Kutzschebauch, Frank.
In: Inventiones Mathematicae, Vol. 181, No. 3, 2010, p. 605-647.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Algebraic volume density property of affine algebraic manifolds
AU - Kaliman, Shulim
AU - Kutzschebauch, Frank
PY - 2010
Y1 - 2010
N2 - We introduce the notion of algebraic volume density property for affine algebraic manifolds and prove some important basic facts about it, in particular that it implies the volume density property. The main results of the paper are producing two big classes of examples of Stein manifolds with volume density property. One class consists of certain affine modifications of ℂn equipped with a canonical volume form, the other is the class of all Linear Algebraic Groups equipped with the left invariant volume form.
AB - We introduce the notion of algebraic volume density property for affine algebraic manifolds and prove some important basic facts about it, in particular that it implies the volume density property. The main results of the paper are producing two big classes of examples of Stein manifolds with volume density property. One class consists of certain affine modifications of ℂn equipped with a canonical volume form, the other is the class of all Linear Algebraic Groups equipped with the left invariant volume form.
UR - http://www.scopus.com/inward/record.url?scp=77954458391&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77954458391&partnerID=8YFLogxK
U2 - 10.1007/s00222-010-0255-x
DO - 10.1007/s00222-010-0255-x
M3 - Article
AN - SCOPUS:77954458391
VL - 181
SP - 605
EP - 647
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
IS - 3
ER -