Positive cones of the projectivization of a parabolic bundle over a curve

2025/06/21 by Bansal, Ashima, Biswas, Indranil, Majumder, Souradeep
#14F05 #14H60 #14L24 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.17594

Abstract

We study the positivity properties of the projectivization of a parabolic bundle over a smooth complex projective curve. The generators of its Néron--Severi group are computed, and the positive cone is determined. In particular, we compute explicitly the generators for the higher nef cones and the pseudoeffective cones. As an application, we deduce a necessary and sufficient condition for the semistability of a parabolic bundle.

Citations

• Effective cones of cycles on products of projective bundles over curves
• Positive cones of dual cycle classes
• Parabolic k-ample bundles
• The cones of effective cycles on projective bundles over curves
• Connections on a parabolic principal bundle, II
• Characterization of Abelian Varieties

Related

• Remarks on the positivity of the cotangent bundle of a K3 surface
• Parabolic Raynaud bundles
• Semistability criterion for parabolic vector bundles on curves
• The very good property for parabolic vector bundles over curves
• Frobenius pull-back of parabolic bundles and dormant opers