Essential normality and the decomposability of algebraic varieties

Matthew Kennedy, Orr Moshe Shalit

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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 normality is preserved by isomorphisms between varieties, and we establish a similar result for maps between varieties that are not necessarily invertible. We also relate the decomposability of an algebraic variety to the problem of establishing the essential normality of the corresponding submodule. These results are applied to prove that the Arveson-Douglas conjecture holds for submodules corresponding to varieties that decompose into linear subspaces, and varieties that decompose into components with mutually disjoint linear spans.

Original languageEnglish
Pages (from-to)877-890
Number of pages14
JournalNew York Journal of Mathematics
Volume18
StatePublished - 20 Oct 2012

Keywords

  • Arveson's conjecture
  • Drury-Arveson space
  • Essential normality

ASJC Scopus subject areas

  • Mathematics (all)

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