{"paper":{"title":"Explicit formulas for infinitely many Shimura curves in genus 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Martin Moeller, Samuel Grushevsky","submitted_at":"2015-10-19T20:29:12Z","abstract_excerpt":"In this paper we construct infinitely many Shimura curves contained in the locus of Jacobians of genus four curves. All Jacobians in these families are ${\\mathbb Z}/3$ covers of varying elliptic curves that appear in a geometric construction of Pirola, and include an example of a Shimura-Teichmuller curve that parameterizes Jacobians that are suitable ${\\mathbb Z}/6$ covers of ${\\mathbb P}^1$. We compute explicitly the period matrices of the Shimura curves we construct using the original construction of Shimura for moduli spaces of abelian varieties with automorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05674","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"}