{"paper":{"title":"The Chow ring of $\\mathcal{S}_5^-$ is tautological","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Bogdan Carasca","submitted_at":"2026-06-13T08:38:24Z","abstract_excerpt":"The moduli spaces $\\mathcal{S}_g^-$ parametrise odd spin curves of genus $g$. These are pairs $[C, \\eta]$ where $C$ is a smooth genus $g$ curve of and $\\eta$ is a line bundle on $C$ such that $\\eta^{\\otimes 2} = \\omega_C$ and $h^0(C, \\eta)$ is odd. The main result of this work is the tautology of the Chow ring of $\\mathcal{S}_5^-$. Our method of proof revolves around an analysis of the geometry of canonical genus 5 curves and totally tangent hyperplanes. In the course of establishing our main result, we also prove the rationality of the closely related differential stratum in $\\mathcal{M}_{5, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.15193","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.15193/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}