{"paper":{"title":"Degree of irrationality of a very general abelian variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elisabetta Colombo, Gian Pietro Pirola, Juan Carlos Naranjo, Olivier Martin","submitted_at":"2019-06-26T19:36:53Z","abstract_excerpt":"Consider a very general abelian variety $A$ of dimension at least $3$ and an integer $0<d\\leq \\dim A$. We show that if the map $A^k\\to CH_0(A)$ has a $d$-dimensional fiber then $k\\geq d+(\\dim A+1)/2$. This extends results of the second-named author which covered the cases $d=1,2$. As a geometric application, we obtain that any dominant rational map from a very general abelian $g$-fold to $\\mathbb{P}^g$ has degree at least $(3\\dim A+1)/2$ for $g\\geq 3$. This improves results of Alzati and the last-named author in the case of a very general abelian variety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11309","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"}