{"paper":{"title":"Isogenous decomposition of the Jacobian of generalized Fermat curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mariela Carvacho, Rub\\'en A. Hidalgo, Sa\\'ul Quispe","submitted_at":"2015-07-10T13:55:44Z","abstract_excerpt":"A closed Riemann surface $S$ is called a generalized Fermat curve of type $(p,n)$, where $p,n \\geq 2$ are integers, if it admits a group $H \\cong {\\mathbb Z}_{p}^{n}$ of conformal automorphisms so that $S/H$ is an orbifold of genus zero with exactly $n+1$ cone points, each one of order $p$. It is known that $S$ is a fiber product of $(n-1)$ classical Fermat curves of degree $p$ and, for $(p-1)(n-1)>2$, that it is a non-hyperelliptic Riemann surface. In this paper, assuming $p$ to be a prime integer, we provide a decomposition, up to isogeny, of the Jacobian variety $JS$ as a product of Jacobia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02903","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"}