The curvature invariant of a Hilbert module over C[z_1,...,z_d]

Details The curvature invariant of a Hilbert module over C[z_1,...,z_d] The curvature invariant of a Hilbert module over C[z_1,...,z_d]

1998-08-23

arxiv.org/abs/math/9808100v1

Mathematics

Operator Algebras

75 pp. AMS-TeX 2.0

Scientific paper

A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established for graded (contractive) Hilbert modules over the complex polynomial algebra in d variables, d=1,2,3,.... The curvature invariant, Euler characteristic, and degree are computed for some explicit examples based on varieties in (multidimensional) complex projective space, and applications are given to the structure of graded ideals in C[z_1,...,z_d] and to the existence of "inner sequences" for closed submodules of the free Hilbert module H^2(C^d).

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