{"paper":{"title":"Fundamental group of a geometric invariant theoretic quotient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. J. Parameswaran, Amit Hogadi, Indranil Biswas","submitted_at":"2014-10-20T05:08:15Z","abstract_excerpt":"Let $M$ be an irreducible smooth projective variety, defined over an algebraically closed field, equipped with an action of a connected reductive affine algebraic group $G$, and let ${\\mathcal L}$ be a $G$--equivariant very ample line bundle on $M$. Assume that the GIT quotient $M/\\!\\!/G$ is a nonempty set. We prove that the homomorphism of algebraic fundamental groups $\\pi_1(M)\\, \\longrightarrow\\, \\pi_1(M/\\!\\!/G)$, induced by the rational map $M\\, \\longrightarrow\\, M/\\!\\!/G$, is an isomorphism.\n  If $k\\,=\\, \\mathbb C$, then we show that the above rational map $M\\, \\longrightarrow \\, M/\\!\\!/G$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5156","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":""},"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"}