A Codimension Two CR Singular Submanifold That Is Formally Equivalent to a Symmetric Quadric

作者：Huang Xiaojun^*; Yin Wanke

来源：International Mathematics Research Notices, 2009, (15): 2789-2828.

DOI：10.1093/imrn/rnp033

Let M subset of C(n 1) (n >= 2) be a real analytic submanifold defined by an equation of the form: w=vertical bar z vertical bar(2) O(vertical bar z vertical bar(3)), where we use (z, w) is an element of C(n) x 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 infinity : w = vertical bar z vertical bar(2,) 0) if and only if it can be formally transformed to (M infinity, 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.

• 出版日期2009
• 单位武汉大学