{"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 $M$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0342","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":""},"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"}