Stable division and essential normality: the non-homogeneous and quasi-homogeneous cases

Shibananda Biswas, Orr Moshe Shalit

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Let H d (t) (t ≥ −d, t > −3) be the reproducing kernel Hilbert space on the unit ball B d with kernel 1 k(z, w) = (1 − h z, wi )d +t+ 1 . We prove that if an ideal I C[z 1 , . . ., z d ] (not necessarily homogeneous) has what we call the approximate stable division property, then the closure of I in H d (t) is p-essentially normal for all p > d. We then show that all quasi-homogeneous ideals in two variables have the stable division property, and combine these two results to obtain a new proof of the fact that the closure of any quasi-homogeneous ideal in C[x, y] is p-essentially normal for p > 2.

Original languageEnglish
Pages (from-to)169-185
Number of pages17
JournalIndiana University Mathematics Journal
Volume67
Issue number1
DOIs
StatePublished - 1 Jan 2018
Externally publishedYes

Keywords

  • Essential normality
  • Groebner basis
  • Hilbert submodules
  • Quasi-homogeneous polynomials

ASJC Scopus subject areas

  • General Mathematics

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