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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Unitary invariants for Hilbert modules of finite rank

1Department of Mathematics, Indian Institute of Science, Bangalore 560012, India

2Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

Citation Information: Journal fr die reine und angewandte Mathematik (Crelles Journal). Volume 2012, Issue 662, Pages 165–204, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2011.091, January 2012

Publication History

Received:
2010-06-07
Revised:
2010-09-10

Abstract

We associate a sheaf model to a class of Hilbert modules satisfying a natural finiteness condition. It is obtained as the dual to a linear system of Hermitian vector spaces (in the sense of Grothendieck). A refined notion of curvature is derived from this construction leading to a new unitary invariant for the Hilbert module. A division problem with bounds, originating in Douady's privilege, is related to this framework. A series of concrete computations illustrate the abstract concepts of the paper.

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