Abstract
On a smooth domain in \({{\mathbb {C}}^n}\) of finite D’Angelo q-type at a point, an effective upper bound for the vanishing order of the Levi determinant \({{\rm coeff}\{\partial r \wedge {\bar \partial} r \wedge (\partial {\bar \partial} r)^{n-q}\}}\) 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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Nicoara, A.C. Effective vanishing order of the Levi determinant. Math. Ann. 354, 1223–1245 (2012). https://doi.org/10.1007/s00208-011-0742-4
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DOI: https://doi.org/10.1007/s00208-011-0742-4