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Kutzschebauch, Frank

Open this publication in new window or tab >>Holomorphic families of non-equivalent embeddings and of holomorphic group actions on affine space### Kutzschebauch, Frank

### Lodin, Sam

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2013 (English)In: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 162, no 1, p. 49-94Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

2 Complex-variables; Intrinsic Measures; Density Property; Stein Manifolds; Oka Principle; Automorphisms; Interpolation; Dimension; C(n); C-2
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-9633 (URN)10.1215/00127094-1958969 (DOI)000314079400002 ()2-s2.0-84873305556 (Scopus ID)
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Available from: 2009-09-15 Created: 2009-09-15 Last updated: 2017-12-13Bibliographically approved

Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.

Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.

We construct holomorphic families of proper holomorphic embeddings of C-k into C-n (0 < k < n - 1), so that for any two different parameters in the family, no holomorphic automorphism of C-n can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of C-n, we derive the existence of families of holomorphic C*-actions on C-n (n >= 5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of C*-actions on C-n (with prescribed linear part at a fixed point).

Open this publication in new window or tab >>Embeddings through Discrete Sets of Discs### Borell, Stefan

### Kutzschebauch, Frank

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2008 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 46, no 2, p. 251-269Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-15026 (URN)10.1007/s11512-008-0079-8 (DOI)
#####

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Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2017-12-08Bibliographically approved

University of Berne Institute of Mathematics Sidlerstrasse 5 CH-3012 Berne Switzerland.

University of Berne Institute of Mathematics Sidlerstrasse 5 CH-3012 Berne Switzerland.

We investigate whether a Stein manifold *M* which allows proper holomorphic embedding into ℂ^{ n } can be embedded in such a way that the image contains a given discrete set of points and in addition follow arbitrarily close to prescribed tangent directions in a neighbourhood of the discrete set. The infinitesimal version was proven by Forstnerič to be always possible. We give a general positive answer if the dimension of *M* is smaller than *n*/2 and construct counterexamples for all other dimensional relations. The obstruction we use in these examples is a certain hyperbolicity condition.

Open this publication in new window or tab >>Proper Holomorphic Disks in the Complement of Varieties in C^{2}### Borell, Stefan

### Kutzschebauch, Frank

### Wold, Erlend Fornæss

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2008 (English)In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 15, no 4, p. 821-826Article in journal (Refereed) Published
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-15027 (URN)
#####

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Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2017-12-08Bibliographically approved

Open this publication in new window or tab >>An interpolation theorem for proper holomorphic embeddings### Forstneric, Franc

### Ivarsson, Björn

### Kutzschebauch, Frank

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2007 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 338, no 3, p. 545-554Article in journal (Refereed) Published
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-9635 (URN)10.1007/s00208-007-0087-1 (DOI)
#####

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Available from: 2009-09-15 Created: 2009-09-15 Last updated: 2017-12-13Bibliographically approved

Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.

Open this publication in new window or tab >>Criteria for the density property of complex manifolds### Kaliman, Shulim

### Kutzschebauch, Frank

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2007 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 172, p. 71-87Article in journal (Refereed) Published
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-9637 (URN)10.1007/s00222-007-0094-6 (DOI)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_j_idt359",{id:"formSmash:j_idt184:4:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt359",multiple:true});
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Available from: 2009-09-15 Created: 2009-09-15 Last updated: 2017-12-13Bibliographically approved

Department of Mathematics, University of Miami.

Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.

Open this publication in new window or tab >>Criteria for the density property of complex manifolds### Kutzschebauch, Frank

### Kaliman, Shulim

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2006 (English)Report (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Bonn: Max-Planck inst, 2006. p. 11
##### Series

Preprints of the Max-Planck-Institut für Mathematik ; 2006-89
##### Keywords

density property
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-5895 (URN)4376 (Local ID)4376 (Archive number)4376 (OAI)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_j_idt359",{id:"formSmash:j_idt184:5:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_j_idt359",multiple:true});
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##### Note

arXiv:0710.3864v1
To appear in Invent MathAvailable from: 2008-09-30 Created: 2009-09-15Bibliographically approved

Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.

In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all linear algebraic groups whose connected components are different from tori or $\C_+$. As another application of this approach we tackle the question (asked among others by F. Forstneri\v{c}) about the density of algebraic vector fields on Euclidean space vanishing on a codimension 2 subvariety.

Open this publication in new window or tab >>Non-equivalent embeddings into complex Euclidean spaces### Borell, Stefan

Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.### Kutzschebauch, Frank

Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2006 (English)In: International Journal of Mathematics, ISSN 0129-167X, Vol. 17, no 9, p. 1033-1046Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

proper holomorphic embeddings, hyperbolicity, Eisenman, complex analysis
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-3420 (URN)10.1142/S0129167X06003795 (DOI)000242603500002 ()2-s2.0-33750928991 (Scopus ID)3404 (Local ID)3404 (Archive number)3404 (OAI)
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Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2017-12-12Bibliographically approved

We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into ℂn. In this paper we prove that if the automorphism group of X is a Lie group and there exists a proper holomorphic embedding of X into ℂn, 0 < dim X < n, then for any k ≥ 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X × ℂk ℂn × ℂk. For k = 0 all embeddings will be proved to satisfy the additional property of ℂn\Φ(X) being (n - dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of ℂk into ℂn whenever 0 < k < n.

Open this publication in new window or tab >>The density property for hypersurfaces uv=p(x)### Kaliman, Shulim

### Kutzschebauch, Frank

Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2006 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, Vol. 258, no 1, p. 115-131Article in journal (Refereed) Published
##### Abstract [en]

##### Series

Max-Planck-Institut Preprint Series 2006 (90)
##### Keywords

density property
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-5894 (URN)10.1007/s00209-007-0162-z (DOI)4375 (Local ID)4375 (Archive number)4375 (OAI)
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Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2011-01-10Bibliographically approved

kaliman@math.miami.edu.

We study hypersurfaces of Cn+2 ¯x,u,v given by equations of form uv = p( ¯x) where the zero locus of a polynomial p is smooth reduced. The main result says that the Lie algebra generated by algebraic completely integrable vector fields on such a hypersurface coincides with the Lie algebra of all algebraic vector fields. Consequences of this result for some conjectures of affine algebraic geometry and for the Oka-Grauert-Gromov principle are discussed.

Open this publication in new window or tab >>An interpolation theorem for proper holomorphic embeddings### Forstneric, Franc

### Ivarsson, Björn

### Kutzschebauch, Frank

Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.### Prezelj, Jasna

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2005 (English)Report (Other academic)
##### Abstract [en]

##### Series

Erwin Schroedinger Institut, preprint ; 1735
##### Keywords

Stein spaces
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-5824 (URN)3494 (Local ID)3494 (Archive number)3494 (OAI)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_j_idt359",{id:"formSmash:j_idt184:8:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt359",multiple:true});
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##### Note

arXiv:math/0511122v3Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2009-09-15Bibliographically approved

Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster.

Open this publication in new window or tab >>Andersén-Lempert-theory with parameters: a representation theoretic point of view### Kutzschebauch, Frank

Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2005 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 4, no 3, p. 325-340Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Andersen-Lempert theory
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:miun:diva-3442 (URN)10.1142/S0219498805001216 (DOI)3478 (Local ID)3478 (Archive number)3478 (OAI)
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Available from: 2008-09-30 Created: 2009-09-15 Last updated: 2017-12-12Bibliographically approved

We calculate the invariant subspaces in the linear representation of the group of algebraic automorphisms of ℂn on the vector space of algebraic vector fields on ℂn and more generally we do this in a setting with parameter. As an application to the field of Several Complex Variables we get a new proof of the Andersén–Lempert observation and a parametric version of the Andersén–Lempert theorem. Further applications to the question of embeddings of ℂk into ℂn are announced.