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arXiv · 1103.1299

Semistability criterion for parabolic vector bundles on curves

Indranil Biswas·Ajneet Dhillon
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Abstract

We give a cohomological criterion for a parabolic vector bundle on a curve to be semistable. It says that a parabolic vector bundle $E$ with rational parabolic weights is semistable if and only if there is another parabolic vector bundle $F$ with rational parabolic weights such that the cohomologies of the vector bundle underlying the para- bolic tensor product $E \otimes F$ vanish. This criterion generalizes the known semistability criterion of Faltings for vector bundles on curves and significantly improves the result in [Bis07].

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Indranil Biswas, Ajneet Dhillon. 2011-10-24. Semistability criterion for parabolic vector bundles on curves. https://arxiv.org/abs/1103.1299

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