The nef and pseudoeffective cones of the projectivization of a parabolic vector bundle over a curve are determined by the parabolic Harder-Narasimhan slopes, yielding a semistability criterion.
Biswas, Parabolic bundles as orbifold bundles,Duke Math
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Positive Cones of the Projectivization of a parabolic vector bundle and Their Products over a Curve
The nef and pseudoeffective cones of the projectivization of a parabolic vector bundle over a curve are determined by the parabolic Harder-Narasimhan slopes, yielding a semistability criterion.