Essential normality and the decomposability of algebraic varieties
arXiv:1207.2808
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.
Final version. 15 pages. http://nyjm.albany.edu/j/2012/18-44.html
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Cited by in corpus (6)
- Spherical Tuples of Hilbert Space Operators
- Berezin quantization of noncommutative projective varieties
- Essential Normality - a Unified Approach in Terms of Local Decompositions
- Geometric Arveson-Douglas Conjecture and Holomorphic Extension
- Geometirc Arveson-Douglas Conjecture - Decomposition of Varieties
- Stable division and essential normality: the non-homogeneous and quasi homogeneous cases