Nonlinearizable CR Automorphisms for Polynomial Models in C^N
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Geometric Analysis |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1007/s12220-022-01144-2 |
| Doi | http://dx.doi.org/10.1007/s12220-022-01144-2 |
| Keywords | Catlin multitype; Polynomial models; Holomorphic vector fields; Infinitesimal CR automorphisms |
| 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. |
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