@article{ba8d78fd249f41198ee0b8bea3911072,
title = "A Codimension two CR singular submanifold that is formally equivalent to a symmetric quadric",
abstract = "Let M ⊂ ℂ n+1 (n ≥ 2) be a real analytic submanifold defined by an equation of the form: w = |z| 2 + O(|z| 3), where we use (z,w) ∈ ℂ n × ℂ for the coordinates of ℂ n+1.We first derive a pseudonormal form for M near 0. We then use it to prove that (M, 0) is holomorphically equivalent to the quadric (M ∞ : w = |z| 2, 0) if and only if it can be formally transformed to (M ∞, 0). We also use it to give a necessary and sufficient condition when (M, 0) can be formally flattened. Our main theorem generalizes a classical result of Moser for the case of n = 1.",
author = "Xiaojun Huang and Wanke Yin",
note = "Funding Information: A part of this work was done when the first author was visiting the School of Mathematics and Statistics, Wuhan University, China, in the summer of 2007, and when the second author was visiting the Mathematical Department of Rutgers University at New Brunswick in March, 2007. The authors would like to thank their corresponding guest institutes for the hospitality during their visit. The authors thank one of the referees for several very helpful comments on the article, which have greatly improved the exposition and the mathematics of the article. This work was supported in part by National Science Foundation (grant no. 0801056).",
year = "2009",
doi = "10.1093/imrn/rnp033",
language = "English (US)",
volume = "2009",
pages = "2789--2828",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "15",
}