{"paper":{"title":"Positive Cones of the Projectivization of a parabolic vector bundle and Their Products over a Curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ashima Bansal, Indranil Biswas, Souradeep Majumder","submitted_at":"2025-06-21T05:19:52Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17594","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.17594/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}