{"paper":{"title":"On surfaces of general type with p_g=q=1 isogenous to a product of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Polizzi","submitted_at":"2006-01-04T11:49:18Z","abstract_excerpt":"A smooth algebraic surface $S$ is said to be \\emph{isogenous to a product of unmixed type} if there exist two smooth curves $C, F$ and a finite group $G$, acting faithfully on both $C$ and $F$ and freely on their product, so that $S=(C \\times F)/G$. In this paper we classify the surfaces of general type with $p_g=q=1$ which are isogenous to an unmixed product, assuming that the group $G$ is abelian. It turns out that they belong to four families, that we call surfaces of type $I, II, III, IV$. The moduli spaces $\\mathfrak{M}_{I},\n  \\mathfrak{M}_{II}, \\mathfrak{M}_{IV}$ are irreducible, whereas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601063","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"}