CR Singularities and Generalizations of Moser's Theorem II

Abstract

Let a real-analytic manifold $M$ formally (holomorphically) equivalent to the following model \begin{equation*}w=z_{1}\overline{z}_{1}+\dots+z_{N}\overline{z}_{N}+λ_{1}\left(z_{1}^{2}+\overline{z}_{1}^{2}\right)+\dots+λ_{N}\left(z_{N}^{2}+\overline{z}_{N}^{2}\right),{equation*} assuming that $${\lambda }_1,\dots ,{\lambda }_N\in \left[0,\frac{1}{2}\right).$$ 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.

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

References in corpus (1)

• Normal forms for CR singular codimension two Levi-flat submanifolds