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Assume that the Futaki invariant relative to G is nondegenerate at g. Consider a smooth family $(M \\to B)$ of polarized complex deformations of (X,\\Omega)\\simeq (M_0,\\Theta_0) provided with a holomorphic action of G with trivial action on B. Then for every t\\in B sufficiently small, there exists an h^{1,1}(X)-dimensional family of extremal Kaehler metrics on M_t whose K\\\"ahler classes are arbitraril"},"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":"1107.0456","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-03T12:59:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"052e93262629d65bc9975e17afa9c2c5b2e2196299dff492cfeab2555a0604f7","abstract_canon_sha256":"1a0634db9dd3ad4b0680ad6725f1ad81a29e920d69b8078573a21b23baf7807a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:35.903405Z","signature_b64":"UeyKVvim3fDAMNOwZ1AxNm6xHHBzPWAmOT89K4BQHkJiDZgkTykkAoUDEx7ymwm8+U6KgZOj0+Ydk6F/ELQPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4939c62d5b5fa18a16fc65742544359899175415e4a3a2afb50024f7f77488e3","last_reissued_at":"2026-05-18T03:34:35.902695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:35.902695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformation of extremal metrics, complex manifolds and the relative Futaki invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Carl Tipler, Santiago R. Simanca, Yann Rollin","submitted_at":"2011-07-03T12:59:00Z","abstract_excerpt":"Let (X,\\Omega) be a closed polarized complex manifold, g be an extremal metric on X that represents the K\\\"ahler class \\Omega, and G be a compact connected subgroup of the isometry group Isom(X,g). Assume that the Futaki invariant relative to G is nondegenerate at g. Consider a smooth family $(M \\to B)$ of polarized complex deformations of (X,\\Omega)\\simeq (M_0,\\Theta_0) provided with a holomorphic action of G with trivial action on B. 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