Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Arveson-Douglas Conjecture and Holomorphic Extension   In this paper we introduce techniques from complex harmonic analysis to prove
a weaker version of the Geometric Arveson-Douglas Conjecture for complex
analytic subsets that is smooth on the boundary of the unit ball and intersects
transversally with it. In fact, we prove that the projection operator onto the
corresponding quotient module is in the Toeplitz algebra
$\mathcal{T}(L^{\infty})$, which implies the essential normality of the
quotient module. Combining some other techniques we actually obtain the
$p$-essential normality for $p>2d$, where $d$ is the complex dimension of the
analytic subset. Finally, we show that our results apply for the closure of a
radical polynomial ideal $I$ whose zero variety satisfies the above conditions.
A key technique is defining a right inverse operator of the restriction map
from the unit ball to the analytic subset generalizing the result of Beatrous's
paper "$L^p$-estimates for extensions of holomorphic functions".

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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an