Normal Forms for Rigid $\mathfrak{C}_{2,1}$ Hypersurfaces $M^5 \subset \mathbb{C}^3$

New Normal Forms for Levi-nondegenerate Hypersurfaces

In this paper we construct a large class of new normal forms for Levi-nondegenerate real hypersurfaces in complex spaces. We adopt a general approach illustrating why these normal forms are natural and which role is played by the celebrated Chern-Moser normal form [CM74]. The latter appears in our class as the one with the ”maximum normalization” in the lowest degree. However, there are other n...

Normal Forms for Hypersurfaces of Finite Type in C2

We construct normal forms for Levi degenerate hypersurfaces of finite type in C. As one consequence, an explicit solution to the problem of local biholomorphic equivalence is obtained. Another consequence determines the dimension of the stability group of the hypersurface.

Birationally rigid Fano hypersurfaces

We prove that a smooth Fano hypersurface V = V M ⊂ P M , M ≥ 6, is birationally superrigid. In particular, it cannot be fibered into uniruled varieties by a non-trivial rational map and each birational map onto a minimal Fano variety of the same dimension is a biregular isomorphism. The proof is based on the method of maximal singularities combined with the connectedness principle of Shokurov a...

Normal Forms of Real Hypersurfaces with Nondegenerate Levi Form

We present a proof of the existence and uniqueness theorem of a normalizing biholomorphic mapping to Chern-Moser normal form. The explicit form of the equation of a chain on a real hyperquadric is obtained. There exists a family of normal forms of real hypersurfaces including Chern-Moser normal form. 0. Introduction Let M be an analytic real hypersurface with nondegenerate Levi form in a comple...

Rigidity Results for Hypersurfaces in Space Forms