{"paper":{"title":"Applications of the affine structures on the Teichm\\\"uller spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kefeng Liu, Xiaojing Chen, Yang Shen","submitted_at":"2014-02-23T01:51:09Z","abstract_excerpt":"We prove the existence of global sections trivializing the Hodge bundles on the Hodge metric completion space of the Torelli space of Calabi--Yau manifolds, a global splitting property of these Hodge bundles. We also prove that a compact Calabi--Yau manifold can not be deformed to its complex conjugate. These results answer certain open questions in the subject. A general result about the period map to be bi-holomorphic from the Hodge metric completion space of the Torelli space of Calabi--Yau type manifolds to their period domains is proved and applied to the cases of K$3$ surfaces, cubic fou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5570","kind":"arxiv","version":4},"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"}