{"paper":{"title":"Condition of intersecting a projective variety with a varying linear subspace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Peter B\\\"urgisser","submitted_at":"2015-10-14T15:14:54Z","abstract_excerpt":"The numerical condition of the problem of intersecting a fixed $m$-dimensional irreducible complex projective variety $Z\\subseteq\\mathbb{P}^n$ with a varying linear subspace $L\\subseteq\\mathbb{P}^n$ of complementary dimension $s=n-m$ is studied. We define the intersection condition number $\\kappa_Z(L,z)$ at a smooth intersection point $z\\in Z\\cap L$ as the norm of the derivative of the locally defined solution map $\\mathbb{G}(s,\\mathbb{P}^n)\\to\\mathbb{P}^n,\\, L\\mapsto z$. We show that $\\kappa_Z(L,z) = 1/\\sin\\alpha$, where $\\alpha$ is the minimum angle between the tangent spaces $T_zZ$ and $T_z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04142","kind":"arxiv","version":3},"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"}