# Geometric Arveson-Douglas Conjecture and Holomorphic Extension

@article{Douglas2015GeometricAC,
title={Geometric Arveson-Douglas Conjecture and Holomorphic Extension},
author={Ronald G. Douglas and Yi Wang},
journal={arXiv: Functional Analysis},
year={2015}
}
• Published 3 November 2015
• Mathematics
• arXiv: Functional Analysis
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…
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