{"paper":{"title":"Tropical Fano Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sara Lamboglia","submitted_at":"2018-07-17T08:54:58Z","abstract_excerpt":"We define a tropical version $\\F_d(\\trop X)$ of the Fano Scheme $\\F_d(X)$ of a projective variety $X\\subseteq \\mathbb P^n$ and prove that $\\F_d(\\trop X)$ is the support of a polyhedral complex contained in $\\trop \\Grp(d,n)$. In general $\\trop \\F_d(X)\\subseteq \\F_d(\\trop X)$ but we construct linear spaces $L$ such that $\\trop \\F_1(X)\\subsetneq \\F_1(\\trop X)$ and show that for a toric variety $\\trop \\F_d(X)=\\F_d(\\trop X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06283","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"}