A Codimension two CR singular submanifold that is formally equivalent to a symmetric quadric

Xiaojun Huang, Wanke Yin

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23 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2789-2828
Number of pages40
JournalInternational Mathematics Research Notices
Volume2009
Issue number15
DOIs
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • General Mathematics

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