New York Journal of Mathematics
Volume 18 (2012) 877-890


Matthew Kennedy and Orr Moshe Shalit

Essential normality and the decomposability of algebraic varieties

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Published: October 20, 2012
Keywords: Essential normality, Arveson's conjecture, Drury-Arveson space
Subject: 47A13, 47A20, 47A99

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.


First author partially supported by NSERC Canada
Second author partially supported by Israel Science Foundation Grant no. 474/12 and by the European Union Seventh Framework Programme ( FP7/2007-2013) under grant agreement no. 321749

Author information

Matthew Kennedy:
School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada

Orr Moshe Shalit:
Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, 84105, Israel