Abstract:We introduce a notion of admissible Hermitian metrics on parabolic bundles and define positivity properties for the same. We develop Chern–Weil theory for parabolic bundles and prove that our metric notions coincide with the already existing algebro-geometric versions of parabolic Chern classes. We also formulate a Griffiths conjecture in the parabolic setting and prove some results that provide evidence in its favor for certain kinds of parabolic bundles. For these kinds of parabolic structures, we prove that… Show more
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