Essential normality of homogenous quotient modules over the polydisc: distinguished variety case

TL;DR

This paper investigates the essential normality of quotient modules over the polydisc, demonstrating that when the zero variety of a homogeneous ideal is a distinguished variety, the quotient module exhibits $(1, ext{infinity})$-essential normality, and explores boundary representations.

Contribution

It establishes the essential normality of quotient modules associated with distinguished varieties in the polydisc, extending understanding of their boundary representations.

Findings

Quotient modules over the polydisc are $(1, ext{infinity})$-essentially normal when associated with distinguished varieties.

The paper characterizes boundary representations of these quotient modules.

Provides new insights into the structure of quotient modules related to homogeneous ideals.

Abstract

In the present paper, we study the essential normality of quotient modules over the polydisc. It is shown that if the zero variety of homogenous ideal $I$ is a distinguished variety, then its quotient module is $(1,\infty)$-essentially normal. Moreover, we study the boundary representation of quotient modules.