{"paper":{"title":"On the direct images of parabolic vector bundles and parabolic connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francois-Xavier Machu, Indranil Biswas","submitted_at":"2018-10-15T23:36:52Z","abstract_excerpt":"Let $\\varphi : Y \\rightarrow X$ be a finite surjective morphism between smooth complex projective curves, where $X$ is irreducible but $Y$ need not be so. Let $V_*$ be a parabolic vector bundle on $Y$. We construct a parabolic structure on the direct image $\\varphi_* V$ on $X$, where $V$ is the vector bundle underlying $V_*$. The parabolic vector bundle $\\varphi_* V_*$ on $X$ obtained this way has a ramified torus sub-bundle; it is a torus bundle of $\\text{Ad}(\\varphi_* V)$ outside the parabolic divisor for $\\varphi_* V_*$ that satisfies certain conditions at the parabolic points. Conversely, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06752","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}