Hilbert polynomials and Arveson's curvature invariant

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We define and study Hilbert polynomials for certain holomorphic Hilbert spaces. We obtain several estimates for these polynomials and their coefficients. Our estimates inspire us to investigate the connection between the leading coefficients of Hilbert polynomials for invariant subspaces of the symmetric Fock space and Arveson's curvature invariant for coinvariant subspaces. We are able to obtain some formulas relating the curvature invariant with other invariants. In particular, we prove that Arveson's version of the Gauss-Bonnet-Chern formula is true when the invariant subspaces are generated by any polynomials.

Original languageEnglish
Pages (from-to)445-464
Number of pages20
JournalJournal of Functional Analysis
Issue number2
StatePublished - 10 Mar 2003


  • Arveson's curvature
  • Gauss-Bonnet-Chern
  • Hilbert module
  • Hilbert polynomial


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