Stable Division and Essential Normality: the Non-homogeneous and Quasi Homogeneous Cases
نویسندگان
چکیده
Let H d (t ≥ −d, t > −3) be the reproducing kernel Hilbert space on the unit ball B d with kernel k(z, w) = 1 (1− 〈z, w〉)d+t+1 . We prove that if an ideal I ⊳ C [z1 , . . . , zd] (not necessarily homogeneous) has what we call the approximate stable division property, then the closure of I in H d is p-essentially normal for all p > d. We then show that all quasi homogeneous ideals in two variables have the stable division property, and combine these two results to obtain a new proof of the fact that the closure of any quasi homogeneous ideal in C [x, y] is p-essentially normal for p > 2.
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