Some Index Formulæ on the Moduli Space of Stable Parabolic Vector Bundles

We study natural families of ∂-operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulæ for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabolic structure. We show that our result implies formulæ for the Chern classes of the associated determinant bundles consistent with a recent result of Takhtajan and Zograf.