Publication details
The equivalence theory for infinite type hypersurfaces in C^2
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | Transactions of the American Mathematical Society |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.ams.org/journals/tran/2022-375-06/S0002-9947-2022-08627-X/ |
| Doi | http://dx.doi.org/10.1090/tran/8627 |
| Keywords | Real submanifolds in complex manifolds; CR manifolds as boundaries of domains |
| Description | We develop a classification theory for real-analytic hypersurfaces in in the case when the hypersurface is of infinite type at the reference point. This is the remaining, not yet understood case in in the Probleme local, formulated by H. Poincaré in 1907 and asking for a complete biholomorphic classification of real hypersurfaces in complex space. One novel aspect of our results is a notion of smooth normal forms for real-analytic hypersurfaces. We rely fundamentally on the recently developed CR-DS technique in CR-geometry. |