Stability of Picard sheaves for vector bundles on curves

For a stable vector bundle E of slope μ(E)>2g−1 on a smooth, projective curve of genus g, we show that the Picard sheaf Eˆ on the Picard variety of the curve is stable. We introduce a homological tool for testing semistability of Picard sheaves. We also obtain the semistability of the general Pic...

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Bibliographic Details
Published in:Journal of geometry and physics 2017-12, Vol.122, p.59-68
Main Authors: Hein, Georg, Ploog, David
Format: Article
Language:English
Subjects:
Picard sheaf
Projective curve
Stability
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Summary:For a stable vector bundle E of slope μ(E)>2g−1 on a smooth, projective curve of genus g, we show that the Picard sheaf Eˆ on the Picard variety of the curve is stable. We introduce a homological tool for testing semistability of Picard sheaves. We also obtain the semistability of the general Picard sheaf if μ(E)∈[g−2,g],μ(E)≠g−1.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2016.12.004