TY - JOUR
T1 - Deformations of CR maps and applications
AU - Della Sala, Giuseppe
AU - Lamel, Bernhard
AU - Reiter, Michael
N1 - Publisher Copyright:
© 2021. International Press
PY - 2022/7/6
Y1 - 2022/7/6
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.
UR - http://www.scopus.com/inward/record.url?scp=85134418087&partnerID=8YFLogxK
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 -