Geometric Arveson-Douglas Conjecture and Holomorphic Extension

  title={Geometric Arveson-Douglas Conjecture and Holomorphic Extension},
  author={Ronald G. Douglas and Yi Wang},
  journal={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… 
Geometric Arveson–Douglas Conjecture-Decomposition of Varieties
In this paper, we prove the Geometric Arveson–Douglas Conjecture for a special case that allows some singularity on $$\partial {\mathbb {B}_n}$$∂Bn. More precisely, we show that if a variety can be
On the $p$-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains
In this paper, we show that under a mild condition, a principal submodule of the Bergman module on a bounded strongly pseudoconvex domain with smooth boundary in $\mathbb{C}^n$ is $p$-essentially
Berezin quantization of noncommutative projective varieties
We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of
Gelfand transforms and boundary representations of complete Nevanlinna–Pick quotients
The main objects under study are quotients of multiplier algebras of certain complete Nevanlinna--Pick spaces, examples of which include the Drury--Arveson space on the ball and the Dirichlet space
Essential normality — a unified approach in terms of local decompositions
  • Yi Wang
  • Mathematics
    Proceedings of the London Mathematical Society
  • 2019
In this paper, we define the asymptotic stable division property for submodules of La2(Bn) . We show that under a mild condition, a submodule with the asymptotic stable division property is p
Essential normality for quotient modules and complex dimensions
The Helton-Howe trace formula for submodules
Toeplitz Operators Associated with Measures and the Dixmier Trace on the Hardy Space
Let $$\mu $$ μ be a regular Borel measure on the open unit ball B in $$\mathbf{C}^n$$ C n . By a natural formula, it gives rise to a Toeplitz operator $$T_\mu $$ T μ on the Hardy space $$H^2(S)$$ H 2
An index theorem for quotients of Bergman spaces on egg domains
In this paper we prove a $K$-homology index theorem for the Toeplitz operators obtained from the multishifts of the Bergman space on several classes of egg-like domains. This generalizes our theorem


An Analytic Grothendieck Riemann Roch Theorem
A new kind of index theorem
Index theory has had profound impact on many branches of mathematics. In this note we discuss the context for a new kind of index theorem. We begin, however, with some operator theoretic results. In
Cycles and relative cycles in analytic $K$-homology
In this paper we continue the study of elliptic operators and ΛMiomology, pursued by the first two authors in [5], [6], [7]. We particularly focus on the concept of relative cycles, their production
Stable polynomial division and essential normality of graded Hilbert modules
It is shown that when the algebra of polynomials in $d$ variables is given the natural $\ell^1$ norm, then every ideal is linearly equivalent to an ideal that has the stable division property.
Localization and Compactness in Bergman and Fock spaces
In this paper we study the compactness of operators on the Bergman space of the unit ball and on very generally weighted Bargmann-Fock spaces in terms of the behavior of their Berezin transforms and
p-Summable Commutators in Dimension d
We show that many invariant subspaces M for d-shifts (S_1,...,S_d) of finite rank have the property that the projection P onto M almost commutes with the S_k in the sense that the commutators PS_k -
Essential normality and the decomposability of algebraic varieties
We consider the Arveson-Douglas conjecture on the essential normality of homogeneous submodules corresponding to algebraic subvarieties of the unit ball. We prove that the property of essential
We discuss the relation between questions regarding the essen- tial normality of finitely generated essentially spherical isometries and some results and conjectures of Arveson and Guo-Wang on the
Geometric Arveson-Douglas conjecture