{"paper":{"title":"Plucker forms and the theta map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Verra, Sonia Brivio","submitted_at":"2009-10-29T12:38:41Z","abstract_excerpt":"In this paper we introduce the elementary notion of Pl\\\"ucker form of a pair $(E,S)$, where $E$ is a vector bundle of rank $r$ on a smooth, irreducible, complex projective variety $X$ and $S \\subset H^0(E)$ is a subspace of dimension $rm$. We apply this notion to the study of theta map $\\theta_r$ on the moduli space $SU_X(r,0)$ of semistable vector bundles of rank $r$ and trivial determinant on a curve $X$ of genus $g$. We prove that $\\theta_r$ is generically injective if $X$ is general and $g >> r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5630","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"}