{"paper":{"title":"Moduli spaces of flat tori with prescribed holonomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Luc Pirio, Selim Ghazouani","submitted_at":"2016-04-06T21:30:35Z","abstract_excerpt":"We generalise to the genus one case several results of Thurston concerning moduli spaces of flat Euclidean structures with conical singularities on the two dimensional sphere.\n  More precisely, we study the moduli space of flat tori with $n$ cone points and a prescribed holonomy $\\rho$. In his paper `Flat Surfaces' Veech has established that under some assumptions on the cone angles, such a moduli space ${\\mathcal{F}}_{[\\rho]}\\subset \\mathscr M_{1,n}$ carries a natural geometric structure modeled on the complex hyperbolic space ${\\mathbb C}{\\mathbb{H} }^{n-1}$ which is not metrically complete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01812","kind":"arxiv","version":2},"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"}