{"paper":{"title":"Symmetric tensors and the geometry of subvarieties of $\\Bbb P^N$","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Bruno De Oliveira, Fedor Bogomolov","submitted_at":"2006-09-18T17:34:20Z","abstract_excerpt":"This paper following a geometric approach proves new, and reproves old, vanishing and nonvanishing results on the space of twisted symmetric differentials, $H^0(X,S^m\\Omega^1_X\\otimes \\Cal O_X(k))$ with $k\\le m$, on subvarieties $X\\subset \\Bbb P^N$. The case of $k=m$ is special and the nonvanishing results are related to the space of quadrics containing $X$ and lead to interesting geometrical objects associated to $X$, as for example the variety of all tangent trisecant lines of $X$. The same techniques give results on the symmetric differentials of subvarieties of abelian varieties. The paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609471","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"}