{"paper":{"title":"On The Global Quotient Structure of The Space of Twisted Stable Maps to a Quotient Stack","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Abramovich, Hsian-Hua Tseng, Martin Olsson, Tom Graber","submitted_at":"2005-02-12T07:12:12Z","abstract_excerpt":"Let $\\mathcal{X}$ be a tame proper Deligne-Mumford stack of the form $[M/G]$ where $M$ is a scheme and $G$ is an algebraic group. We prove that the stack $\\mathcal{K}_{g,n}(\\mathcal{X},d)$ of twisted stable maps is a quotient stack and can be embedded into a smooth Deligne-Mumford stack. When $G$ is finite, we give a more precise construction of $\\mathcal{K}_{g,n}(\\mathcal{X},d)$ using Hilbert schemes and admissible $G$-covers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502253","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"}