{"paper":{"title":"On the number of flats tangent to convex hypersurfaces in random position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Antonio Lerario, Khazhgali Kozhasov","submitted_at":"2017-02-21T18:46:31Z","abstract_excerpt":"We investigate the problem of the number of flats simultaneously tangent to several convex hypersurfaces in real projective space from a random point of view. More precisely, we say that smooth convex hypersurfaces $X_1, \\ldots, X_{d_{k,n}}\\subset \\mathbb{R}\\textrm{P}^n$, where $d_{k,n}=(k+1)(n-k)$, are in random position if each one of them is randomly translated by elements $g_1, \\ldots, g_{{d_{k,n}}}$ sampled independently and uniformly from the Orthogonal group; we denote by $\\tau_k(X_1, \\ldots, X_{d_{k,n}})$ the average number of $k$-dimensional projective subspaces (flats) which are simu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06518","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"}