Semistability criterion for parabolic vector bundles on curves

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].

7 pages

References in corpus (1)

• Fibrés paraboliques et champ des racines

Cited by in corpus (1)

• Root stacks, principal bundles and connections