Singular Hilbert modules on Jordan-Kepler varieties

2019/05/08 by Gadadhar Misra, Misra, Gadadhar, Harald Upmeier +1
Mathematics · #17C36 #46E22 #47B35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Primary 32M15 #Secondary 14M12

paper · pdf · doi:10.48550/arxiv.1905.03284

openalex publication_date 2019/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study submodules of analytic Hilbert modules defined over certain algebraic varieties in bounded symmetric domains, the so-called Jordan-Kepler varieties V_ℓ of arbitrary rank ℓ. For ℓ>1 the singular set of V_ℓ 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.

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