Positive Cones of the Projectivization of a parabolic vector bundle and Their Products over a Curve

Ashima Bansal; Indranil Biswas; Souradeep Majumder

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arXiv · 2506.17594

Positive Cones of the Projectivization of a parabolic vector bundle and Their Products over a Curve

Ashima Bansal·Indranil Biswas·Souradeep Majumder

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Abstract

We compute the positive cones of the projectivization of a parabolic vector bundle and the fiber product of two parabolic projective bundles over a smooth complex projective curve. Specifically, we determine their N\'eron--Severi groups and compute their nef and pseudoeffective cones. Moreover, for the projectivization of a parabolic vector bundle, we explicitly describe the generators of the higher nef and pseudoeffective cones. As an application, we obtain a necessary and sufficient criterion for the semistability of a parabolic vector bundle.

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Ashima Bansal, Indranil Biswas, Souradeep Majumder. 2025-06-21. Positive Cones of the Projectivization of a parabolic vector bundle and Their Products over a Curve. https://arxiv.org/abs/2506.17594

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