{"paper":{"title":"Techniques of computations of Dolbeault cohomology of solvmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Hisashi Kasuya","submitted_at":"2011-07-24T15:10:57Z","abstract_excerpt":"We consider semi-direct products $\\C^{n}\\ltimes_{\\phi}N$ of Lie groups with lattices $\\Gamma$ such that $N$ are nilpotent Lie groups with left-invariant complex structures. We compute the Dolbeault cohomology of direct sums of holomorphic line bundles over $G/\\Gamma$ by using the Dolbeaut cohomology of the Lie algebras of the direct product $\\C^{n}\\times N$. As a corollary of this computation, we can compute the Dolbeault cohomology $H^{p,q}(G/\\Gamma)$ of $G/\\Gamma$ by using a finite dimensional cochain complexes. Computing some examples, we observe that the Dolbeault cohomology varies for cho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4761","kind":"arxiv","version":3},"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"}