Effective vanishing order of the Levi determinant

Details Effective vanishing order of the Levi determinant Effective vanishing order of the Levi determinant

2011-02-02

arxiv.org/abs/1102.0356v2

Mathematics

Complex Variables

22 pages; typos in example from p.20 fixed in the second version

Scientific paper

On a smooth domain in complex n space of finite D'Angelo q-type at a point, an effective upper bound for the vanishing order of the Levi determinant $\text{coeff}\{\partial r \wedge \dbar r \wedge (\partial \dbar r)^{n-q}\}$ at that point is given in terms of the D'Angelo q-type, the dimension of the space n, and q itself. The argument uses Catlin's notion of a boundary system as well as techniques pioneered by John D'Angelo.

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