Deformations of CR maps and applications

Giuseppe Della Sala; Bernhard Lamel; Michael Reiter

doi:10.4310/AJM.2021.v25.n5.a3

Deformations of CR maps and applications

Giuseppe Della Sala, Bernhard Lamel, Michael Reiter

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We study the deformation theory of CR maps in the positive codimensional case. In particular, we study structural properties of the mapping locus E of (germs of nondegenerate) holomorphic maps H: (M, p) → M' between generic real submanifolds M ⊂ CN and M ⊂ CN, defined to be the set of points p'∈ M'which admit such a map with H(p) = p. We show that this set E is semi-analytic and provide examples for which E possesses (prescribed) singularities.

Original language	English
Pages (from-to)	665-682
Number of pages	18
Journal	Asian Journal of Mathematics
Volume	25
Issue number	5
Early online date	2021
DOIs	https://doi.org/10.4310/AJM.2021.v25.n5.a3
Publication status	Published - 6 Jul 2022

Austrian Fields of Science 2012

101009 Geometry

Keywords

Cr maps
Deformations of cr manifolds
Jet parametrization property
Mapping locus
Semi-analytic sets.

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10.4310/AJM.2021.v25.n5.a3

Cite this

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AU - Della Sala, Giuseppe

AU - Lamel, Bernhard

AU - Reiter, Michael

PY - 2022/7/6

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N2 - We study the deformation theory of CR maps in the positive codimensional case. In particular, we study structural properties of the mapping locus E of (germs of nondegenerate) holomorphic maps H: (M, p) → M' between generic real submanifolds M ⊂ CN and M ⊂ CN, defined to be the set of points p'∈ M'which admit such a map with H(p) = p. We show that this set E is semi-analytic and provide examples for which E possesses (prescribed) singularities.

AB - We study the deformation theory of CR maps in the positive codimensional case. In particular, we study structural properties of the mapping locus E of (germs of nondegenerate) holomorphic maps H: (M, p) → M' between generic real submanifolds M ⊂ CN and M ⊂ CN, defined to be the set of points p'∈ M'which admit such a map with H(p) = p. We show that this set E is semi-analytic and provide examples for which E possesses (prescribed) singularities.

KW - Cr maps

KW - Deformations of cr manifolds

KW - Jet parametrization property

KW - Mapping locus

KW - Semi-analytic sets.

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U2 - 10.4310/AJM.2021.v25.n5.a3

DO - 10.4310/AJM.2021.v25.n5.a3

M3 - Article

SN - 1093-6106

VL - 25

SP - 665

EP - 682

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

IS - 5

ER -

Deformations of CR maps and applications

Abstract

Austrian Fields of Science 2012

Keywords

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