{"paper":{"title":"Canonical factorization of the quotient morphism for an affine $\\mathbb{G}_a$-variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gene Freudenburg","submitted_at":"2016-02-28T23:59:13Z","abstract_excerpt":"Working over a ground field of characteristic zero, this paper studies the quotient morphism $\\pi :X\\to Y$ for an affine $\\mathbb{G}_a$-variety $X$ with affine quotient $Y$. It is shown that the degree modules associated to the $\\mathbb{G}_a$-action give a uniquely determined sequence of dominant $\\mathbb{G}_a$-equivariant morphisms, $X=X_r\\to X_{r-1}\\to\\cdots\\to X_1\\to X_0=Y$, where $X_i$ is an affine $\\mathbb{G}_a$-variety and $X_{i+1}\\to X_i$ is birational for each $i\\ge 1$. This is the canonical factorization of $\\pi$. We give an algorithm for finding the degree modules associated to the g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08786","kind":"arxiv","version":3},"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"}