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Metric Properties of Parabolic Ample Bundles

Biswas, I and Pingali, VP (2018) Metric Properties of Parabolic Ample Bundles. In: International Mathematics Research Notices, 2020 (23). pp. 9336-9369.

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Official URL: https://dx.doi.org/10.1093/imrn/rny259


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 the conjecture holds on Riemann surfaces. We also prove that a Berndtsson-type result holds and that there are metrics on stable bundles over surfaces whose Schur forms are positive. © 2018 The Author(s). Published by Oxford University Press. All rights reserved.

Item Type: Journal Article
Publication: International Mathematics Research Notices
Publisher: Oxford University Press
Additional Information: Copyright to this article belongs to Oxford University Press
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 05 Feb 2021 06:40
Last Modified: 05 Feb 2021 06:40
URI: http://eprints.iisc.ac.in/id/eprint/67885

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