{"paper":{"title":"Irreducible components of moduli spaces of maps to smooth projective toric varieties in genus 0","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alberto Cobos Rabano, Etienne Mann","submitted_at":"2025-06-19T11:25:35Z","abstract_excerpt":"We give a combinatorial description of the irreducible components of the moduli space $\\overline{\\mathcal{M}}_{0,n}(X,\\beta)$ for a smooth projective toric variety $X$. The result is based on the study of the irreducible components of an abelian cone over a smooth Noetherian Artin stack. We give concrete applications of the result including $\\overline{\\mathcal{M}}_{0,0}(Bl_{pt} \\mathbb{P}^2,2\\ell)$, where we also describe the main component. This is the first example where the smoothable locus of $\\overline{\\mathcal{M}}_{g,n}(X,\\beta)$ is described for $X$ not a projective space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16221","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.16221/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"}