Singular Hilbert modules on Jordan-Kepler varieties

DOI10.1007/978-3-030-43380-2_20zbMATH Open1462.32027arXiv1905.03284OpenAlexW2943925329MaRDI QIDQ2220167

Harald Upmeier, Gadadhar Misra

Publication date: 21 January 2021

Abstract: We study submodules of analytic Hilbert modules defined over certain algebraic varieties in bounded symmetric domains, the so-called Jordan-Kepler varieties $V_{e}ll$ of arbitrary rank $ell.$ For $ell>1$ the singular set of $V_{e}ll$ 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.

Full work available at URL: https://arxiv.org/abs/1905.03284

zbMATH Keywords

rigiditycurvaturereproducing kernelalgebraic varietysymmetric domainanalytic Hilbert module

Mathematics Subject Classification ID

Determinantal varieties (14M12) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Associated manifolds of Jordan algebras (17C36)

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