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We study and describe explicitly the torsion subsheaf $\\mathrm{Tors}(R^1\\pi_*({\\cal E}))$ of the first direct image $R^1\\pi_*(\\mathcal{E})$ under the assumption $R^0\\pi_*(\\mathcal{E})=0$. We give two applications of our results. The first concerns the locus of points in the base of a generically versal family of complex surfaces where the family is non-versal. The second application is a vanishing result for $H^0(\\mathrm{Tors}(R^1\\pi_*(\\mathcal{E})))$ in a concrete situatio"},"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":"1309.0342","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-09-02T10:00:30Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"0efa09f7bcf21458157342241afb70098ceca35ac235a7143c55a33b44072d45","abstract_canon_sha256":"82cf52f2aef2b0db4c21282b0d342742beea0fbba0505c46fd636a52a1ed3e4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:53.074038Z","signature_b64":"ewiiehPeVOJ0fC4ntDHahPR2Q4rmHZhMslModSPULbRTKSiplDiutj4EZmr2mRDf/JpbRQ6GMLBTw5t1BXU6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e2f58f0cb0fecdf6b6d3220ace655352a77623a415ec2e51c79e947ae73b90f","last_reissued_at":"2026-05-18T02:26:53.073624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:53.073624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the torsion of the first direct image of a locally free sheaf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.CV","authors_text":"Andrei Teleman","submitted_at":"2013-09-02T10:00:30Z","abstract_excerpt":"Let $\\pi:M\\to B$ be a proper holomorphic submersion between complex manifolds and ${\\cal E}$ a holomorphic bundle on $M$. 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