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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, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.06752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-10-15T23:36:52Z","cross_cats_sorted":[],"title_canon_sha256":"43b52a6ad8b4f847375f32cd59c0143fab5e50192ccbbc8254b699275d565430","abstract_canon_sha256":"5791c5079b5cf4695fa54617321a07b7afbc8651e0fd4246ff6d6a5d47810714"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:14.008257Z","signature_b64":"sPmLW3LSQwVgEop2PbZO5XUaZ+5ZwF1sQJC25v1IKWwos/wKuiQeIMlDhi7Y7OlDJ+nD0vsu2j7Dt3ChhQNUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fadf61e8941aaf802bdba3bead3f7934ca3074eae24556896cf426a137453004","last_reissued_at":"2026-05-17T23:59:14.007647Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:14.007647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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