Unitary invariants for Hilbert modules of finite rank

Shibananda Biswas 1 , Gadadhar Misra 1 , and Mihai Putinar 2
  • 1 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
  • 2 Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

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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