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@article{2339958,
author = {Kolář, Martin and Meylan, Francine},
article_number = {3},
doi = {http://dx.doi.org/10.1007/s12220-022-01144-2},
keywords = {Catlin multitype; Polynomial models; Holomorphic vector fields; Infinitesimal CR automorphisms},
language = {eng},
issn = {1050-6926},
journal = {Journal of Geometric Analysis},
title = {Nonlinearizable CR Automorphisms for Polynomial Models in C^N},
url = {https://doi.org/10.1007/s12220-022-01144-2},
volume = {33},
year = {2023}
}
TY - JOUR
ID - 2339958
AU - Kolář, Martin - Meylan, Francine
PY - 2023
TI - Nonlinearizable CR Automorphisms for Polynomial Models in C^N
JF - Journal of Geometric Analysis
VL - 33
IS - 3
SP - 1-25
EP - 1-25
PB - Springer
SN - 10506926
KW - Catlin multitype
KW - Polynomial models
KW - Holomorphic vector fields
KW - Infinitesimal CR automorphisms
UR - https://doi.org/10.1007/s12220-022-01144-2
N2 - The Lie algebra of infinitesimal CR automorphisms is a fundamental local invariant of a CR manifold. Motivated by the Poincaré local equivalence problem, we analyze its positively graded components, containing nonlinearizable holomorphic vector fields. The results provide a complete description of invariant weighted homogeneous polynomial models in C^N, which admit symmetries of degree higher than two. For homogeneous polynomial models, symmetries with quadratic coefficients are also classified completely. As a consequence, this provides an optimal 1-jet determination result in the general case. Further we prove that such automorphisms arise from one common source, by pulling back via a holomorphic mapping a suitable symmetry of a hyperquadric in some (typically high dimensional) complex space.
ER -
KOLÁŘ, Martin and Francine MEYLAN. Nonlinearizable CR Automorphisms for Polynomial Models in C\^{}N. \textit{Journal of Geometric Analysis}. Springer, 2023, vol.~33, No~3, p.~1-25. ISSN~1050-6926. Available from: https://dx.doi.org/10.1007/s12220-022-01144-2.
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