arXiv subjects
Publications and source records attributed to M. A. Stepanova.
New biholomorphic invariants of a germ of a real-analytic set at a singular point (either an RC-singular point or a singular point of a smooth structure) are found: the Bloom-Graham singular type and the singular l-type. Their construction is based on the Bloom-Graham type and l-type constructions, respectively. A series of examples is considered.
The dimension conjecture in CR geometry is proved for 2-nondegenerate real-analytic hypersurfaces with sign-definite Levi form. Namely, it is proved that, in the indicated class of hypersurfaces in $\mathbb{C}^{N}$, the maximum dimension of finite-dimensional Lie algebras of infinitesimal holomorphic automorphisms is strictly smaller than the corresponding dimension for nondegenerate hyperquadrics in $\mathbb{C}^{N}$.