Nonlinearizable CR Automorphisms for Polynomial Models in C^N

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134292" target="_blank" >RIV/00216224:14310/23:00134292 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s12220-022-01144-2" target="_blank" >https://doi.org/10.1007/s12220-022-01144-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s12220-022-01144-2" target="_blank" >10.1007/s12220-022-01144-2</a>

Result language
angličtina
Original language name
Nonlinearizable CR Automorphisms for Polynomial Models in C^N
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA21-09220S" target="_blank" >GA21-09220S: Invariants and symmetries of Levi degenerate CR manifolds</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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