## Semistability Criterion for Parabolic Vector Bundles on Curves

J. Math. Sci. Univ. Tokyo
Vol. 18 (2011), No. 2, Page 181--191.

Biswas, Indranil; Dhillon, Ajneet
Semistability Criterion for Parabolic Vector Bundles on Curves
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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 $\sE_*$ with rational parabolic weights is semistable if and only if there is another parabolic vector bundle $\sF_*$ with rational parabolic weights such that the cohomologies of the vector bundle underlying the parabolic tensor product $\sE_*\otimes\sF_*$ vanish. This criterion generalizes the known semistability criterion of Faltings for vector bundles on curves and significantly improves the result in [Bis07].

Keywords: Parabolic bundle, root stack, semistability, cohomology.

Mathematics Subject Classification (2010): Primary 14F05, Scondary 14H60.
Received: 2011-03-07