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We show that as $t\\rightarrow 0$, $(\\mathcal{X}_t, g_t)$ converges in pointed Gromov-Hausdorff topology to a unique finite disjoint union of complete metric length spaces $\\coprod_{\\alpha=1}^\\mathcal{A} (Y_\\alpha, d_\\alpha)$ without loss of volume. Each $(Y_\\alpha, d_\\alpha)$ is a smooth open K\\\"ahler-Einstein manifold of "},"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":"1706.01518","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-05T19:56:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a7f0721e85ff544c47645fe68924238feb35f3fbaa817a6bd1f06b4e0428d17b","abstract_canon_sha256":"6e3561ade864fabdcfc4efe60989ad4f62a683f44fbc894de20313e8527cb7a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:56.807308Z","signature_b64":"RKSL+6FzBCMlxikpwJbc/xF0B8/yKnRrE1G923ub79sXm02OR8k8qh4/S2beoxkgx5RFymNEApaPFJFhcSd4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3495eb2a01d3a386e2afbfa2fdaffc0385c8b23b1fd96a35b7a0e2ec3805b513","last_reissued_at":"2026-05-18T00:42:56.806614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:56.806614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degeneration of Kahler-Einstein manifolds of negative scalar curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Jian Song","submitted_at":"2017-06-05T19:56:10Z","abstract_excerpt":"Let $\\pi: \\mathcal{X}^* \\rightarrow B^*$ be an algebraic family of compact K\\\"ahler manifolds of complex dimension $n$ with negative first Chern class over a punctured disc $B^*\\in \\mathbb{C}$. Let $g_t$ be the unique K\\\"ahler-Einstein metric on $\\mathcal{X}_t= \\pi^{-1}(t)$. We show that as $t\\rightarrow 0$, $(\\mathcal{X}_t, g_t)$ converges in pointed Gromov-Hausdorff topology to a unique finite disjoint union of complete metric length spaces $\\coprod_{\\alpha=1}^\\mathcal{A} (Y_\\alpha, d_\\alpha)$ without loss of volume. 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