Perturbations of principal submodules in the Drury-Arveson space

Abstract

We study the geometry in the perturbations of principal submodules in the Drury-Arveson space. We show that the perturbations give rise to smooth vector bundles of Hilbert spaces which are equipped with natural Hermitian connections. We compute the associated parallel transport operators and explore properties of the monodromy.1 The smoothness of the vector bundle will be established in Theorem 2.3. 2 Namely, we are momentarily putting aside continuity or smoothness considerations.C such that limn→∞ an/bn = C.