{"paper":{"title":"On the connectedness of the set of Riemann surfaces with real moduli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antonio F. Costa, Ruben A. Hidalgo","submitted_at":"2017-10-12T17:27:27Z","abstract_excerpt":"The moduli space ${\\mathcal{M}}_{g}$, of genus $g\\geq2$ closed Riemann surfaces, is a complex orbifold of dimension $3(g-1)$ which carries a natural real structure i.e. it admits an anti-holomorphic involution $\\sigma$. The involution $\\sigma$ maps each point corresponding to a Riemann surface $S$ to its complex conjugate $\\overline{S}$. The fixed point set of $\\sigma$ consists of the isomorphism classes of closed Riemann surfaces admitting an anticonformal automorphism. Inside $\\mathrm{Fix}(\\sigma)$ is the locus ${\\mathcal{M}}_{g}(\\mathbb{R})$, the set of real Riemann surfaces, which is known"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04627","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"}