Geometric Arveson-Douglas conjecture for the Drury-Arveson space: The case of one-dimensional variety

We consider a class of analytic subsets M˜ of an open neighborhood of the closed unit ball in Cn. Such an M˜ gives rise to a submodule R and a quotient module Q of the Drury-Arveson module Hn2 in n variables. The geometric Arveson-Douglas conjecture predicts that the quotient module Q is p-essential...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 440; p. 109525
Main Author Xia, Jingbo
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2024
Subjects
Drury-Arveson space
Essential normality
Quotient module
Essential normality
Drury-Arveson space
Quotient module
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Summary:We consider a class of analytic subsets M˜ of an open neighborhood of the closed unit ball in Cn. Such an M˜ gives rise to a submodule R and a quotient module Q of the Drury-Arveson module Hn2 in n variables. The geometric Arveson-Douglas conjecture predicts that the quotient module Q is p-essentially normal for p>d=dimCM˜. We prove this conjecture for the case of dimension d=1. In fact, we prove that if d=1, then Q is 1-essentially normal, which is a stronger result than the original prediction.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2024.109525