Abstract
This paper generalizes the index-theoretic content of the physical models studied in [3, 7]. The paper calculates the homology Chern character, and thus the index formula, for a broad class of perturbed Dolbeault operators on complete noncompact complex manifolds. The manifolds studied are complements of smooth polar divisors of meromorphic sections of vector bundles over closed complex manifolds. These sections define complexes of Koszul type that are used to construct the perturbations of the Dolbeault operators.
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