{"paper":{"title":"Quasiplatonic curves with symmetry group ${\\mathbb Z}_{2}^{2} \\rtimes {\\mathbb Z}_{m}$ are definable over ${\\mathbb Q}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Leslie Jim\\'enez, Rub\\'en A. Hidalgo, Sa\\'ul Quispe, Sebasti\\'an Reyes-Carocca","submitted_at":"2016-04-03T23:34:27Z","abstract_excerpt":"It is well known that every closed Riemann surface $S$ of genus $g \\geq 2$, admitting a group $G$ of conformal automorphisms so that $S/G$ has triangular signature, can be defined over a finite extension of ${\\mathbb Q}$. It is interesting to know, in terms of the algebraic structure of $G$, if $S$ can in fact be defined over ${\\mathbb Q}$. This is the situation if $G$ is either abelian or isomorphic to $A \\rtimes {\\mathbb Z}_{2}$, where $A$ is an abelian group. On the other hand, as shown by Streit and Wolfart, if $G = {\\mathbb Z}_{p} \\rtimes {\\mathbb Z}_{q}$ where $p,q>3$ are prime integers,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00702","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"}