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Unitary Invariants For Hilbert Modules of Finite Rank
|Title||Unitary Invariants For Hilbert Modules of Finite Rank|
|Publication Type||Journal Article|
|Year of Publication||2012|
|Authors||Biswas, S, Misra, G, Putinar, M|
|Journal||Journal Fur Die Reine Und Angewandte Mathematik|
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.