{"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. Each $(Y_\\alpha, d_\\alpha)$ is a smooth open K\\\"ahler-Einstein manifold of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01518","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"}