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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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 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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