Essentially normal quotient weighted Bergman modules over the bidisk and distinguished varieties

We introduce a Grassmannian structure for a class of quotient Hilbert modules and attack the polydisc version of ArvesonDouglas conjecture associated to distinguished varieties. More interestingly, we obtain an operator-theoretic characterization of distinguished varieties in the bidisk in terms of essential normality of the quotient modules. As an application, we study the K-homology of the boundary of distinguished variety.& COPY; 2023 Elsevier Inc. All rights reserved.