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Semistability Criterion for Parabolic Vector Bundles on Curves

By Indranil Biswas and Ajneet Dhillon

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 parabolic tensor product E* ⊗ F* vanish. This criterion generalizes the known semistability criterion of Faltings for vector bundles on curves and significantly improves the result in [Bis07]

Topics: Parabolic bundle, root stack, semistability, cohomology, 415, 14F05(MSC2010), 14H60(MSC2010)
Publisher: Department of Mathematics, University of Western Ontario
Year: 2011
OAI identifier: oai:repository.dl.itc.u-tokyo.ac.jp:2261/52705
Provided by: UT Repository
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