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The Riemann--Hilbert correspondence produces a biholomorphism between the moduli space ${\\mathcal M}_X(G)$ parametrizing holomorphic $G$--connections on $X$ and the $G$--character variety $${\\mathcal R}(G):= \\text{Hom}(\\pi_1(X, x_0), G)/\\!\\!/G\\, .$$ While ${\\mathcal R}(G)$ is known to be affine, we show that ${\\mathcal M}_X(G)$ is not affine. The scheme ${\\mathcal R}(G)$ has an algebraic symplectic form constructed by Goldman. We construct an algebraic symplectic f"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.03906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-08T09:31:01Z","cross_cats_sorted":[],"title_canon_sha256":"460792b68c8285d83dd2d5a4d38ecff07502f379adbad4163df93031f6f05f3d","abstract_canon_sha256":"aa9dd74bd222d4bd9ea627a954febbbcb9a231a6a06ccf23cebe8e75e0939b6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:07.736297Z","signature_b64":"xqcGwgiboJuS2fhA+6Xv9DCP8N+q72hs3J1wG4XglcKYmOYSlHRTB81tsN8M+DYQvVkO0Gr96o6iny+KfhYlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63f39ba54e93c6e4c2168f818733c695a03d775d7d91106504f50af7d647dd8e","last_reissued_at":"2026-05-17T23:49:07.735548Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:07.735548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the moduli space of holomorphic G-connections on a compact Riemann surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Indranil Biswas","submitted_at":"2019-04-08T09:31:01Z","abstract_excerpt":"Let $X$ be a compact connected Riemann surface of genus at least two and $G$ a connected reductive complex affine algebraic group. The Riemann--Hilbert correspondence produces a biholomorphism between the moduli space ${\\mathcal M}_X(G)$ parametrizing holomorphic $G$--connections on $X$ and the $G$--character variety $${\\mathcal R}(G):= \\text{Hom}(\\pi_1(X, x_0), G)/\\!\\!/G\\, .$$ While ${\\mathcal R}(G)$ is known to be affine, we show that ${\\mathcal M}_X(G)$ is not affine. The scheme ${\\mathcal R}(G)$ has an algebraic symplectic form constructed by Goldman. 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