Metric Properties of Parabolic Ample Bundles

Author:

Biswas Indranil12,Pingali Vamsi Pritham3

Affiliation:

1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, India

2. Mathematics Department, EISTI-University Paris-Seine, Avenue du Parc, Cergy-Pontoise, France

3. Department of Mathematics, Indian Institute of Science, Bangalore, India

Abstract

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.

Funder

Science and Engineering Research Board

University Grants Commission

Infosys Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

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