Misra, G and Upmeier, H (2020) Singular Hilbert Modules on Jordan–Kepler Varieties. [Book Chapter]
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Official URL: https://doi.org/10.1007/978-3-030-43380-2_20
Abstract
We study submodules of analytic Hilbert modules defined over certain algebraic varieties in bounded symmetric domains, the so-called Jordan–Kepler varieties Vℓ of arbitrary rank ℓ. For ℓ > 1, the singular set of Vℓ is not a complete intersection. Hence the usual monoidal transformations do not suffice for the resolution of the singularities. Instead, we describe a new higher rank version of the blow-up process, defined in terms of Jordan algebraic determinants, and apply this resolution to obtain the rigidity of the submodules vanishing on the singular set.
| Item Type: | Book Chapter |
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| Publication: | Operator Theory: Advances and Applications |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Algebraic variety; Analytic Hilbert module; Curvature; Reproducing kernel; Rigidity; Symmetric domain |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 23 Jan 2023 10:02 |
| Last Modified: | 23 Jan 2023 10:02 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79261 |
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