The Dimension Conjecture for 2-Nondegenerate Hypersurfaces

M. A. Stepanova

The Dimension Conjecture for 2-Nondegenerate Hypersurfaces

Complex Variables 2026-07-21 v1

Authors: M. A. Stepanova

Abstract

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 $\mathbb{C}^{N}$ .

Keywords

dimension conjecture CR geometry 2-nondegenerate hypersurfaces Levi form holomorphic automorphisms

Cite

@article{arxiv.2607.19186,
  title  = {The Dimension Conjecture for 2-Nondegenerate Hypersurfaces},
  author = {M. A. Stepanova},
  journal= {arXiv preprint arXiv:2607.19186},
  year   = {2026}
}