CR Singularities and Generalizations of Moser's Theorem II

2019/06/12 by Valentin Burcea, Burcea, Valentin · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV

paper · pdf · doi:10.48550/arxiv.1906.05313

70 pages. Very close to its final version. I have read it for more times, becuase I will probably add more reshaped results

openalex publication_date 2019/06/12 · arxiv created 2021/05/31 · arxiv updated 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a real-analytic manifold M formally (holomorphically) equivalent to the following model \beginequation*w=z₁z₁+…+z_Nz_N+λ₁(z₁²+z₁²)+…+λ_N(z_N²+z_N²),equation* assuming that λ₁,…, λ_N∈ [0,(1)/(2)). It is proven that M is holomorphically equivalent to this model by developing a partial normal form for such real-analytic submanifold using generalized Fischer Decompositions. In particular, there are defined certain Spaces of Normalizations used also in proving other analogues of The Theorem of Moser in certain non-equidimensional situations. There presented also other applications for the methods considered.

Citations

• On Stein neighborhood basis of real surfaces

Cited by

• Special Classes of CR Singularities I

Related

• Special Classes of CR Singularities I
• CR Singularities and Generalizations of Moser's Theorem I
• A codimension two CR singular submanifold that is formally equivalent to a symmetric quadric
• Real Submanifolds in Complex Spaces: Upgrades
• Equivalences of 5-dimensional CR manifolds III: Six models and elementary normalizations