Representability of Chern–Weil forms

In this paper we look at two naturally occurring situations where the following question arises. When one can find a metric so that a Chern–Weil form can be represented by a given form? The first setting is semi-stable Hartshorne-ample vector bundles on complex surfaces where we provide evidence for...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2018-02, Vol.288 (1-2), p.629-641
Main Author: Pingali, Vamsi Pritham
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Riemann surfaces
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Summary:In this paper we look at two naturally occurring situations where the following question arises. When one can find a metric so that a Chern–Weil form can be represented by a given form? The first setting is semi-stable Hartshorne-ample vector bundles on complex surfaces where we provide evidence for a conjecture of Griffiths by producing metrics whose Chern forms are positive. The second scenario deals with a particular rank-2 bundle (related to the vortex equations) over a product of a Riemann surface and the sphere.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-017-1903-2