{"paper":{"title":"The jumping phenomenon of the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jiezhu Lin, Xuanming Ye","submitted_at":"2014-03-03T00:56:44Z","abstract_excerpt":"Let $X$ be a compact complex manifold, and let $\\pi: \\mathcal{X} \\rightarrow B$ be a small deformation of $X$, the dimensions of the Bott-Chern cohomology groups $H_{\\rm BC}^{p,q}(X(t))$ and Aeppli cohomology groups $H_{\\rm A}^{p,q}(X(t))$ may vary under this deformation. In this paper, we will study the deformation obstructions of a $(p,q)$ class in the central fiber $X$. In particular, we obtain an explicit formula for the obstructions and apply this formula to the study of small deformations of the Iwasawa manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0285","kind":"arxiv","version":2},"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"}