{"paper":{"title":"Hamiltonian $2$-forms and new explicit Calabi--Yau metrics and gradient steady K\\\"ahler--Ricci solitons on $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Charles Cifarelli, Vestislav Apostolov","submitted_at":"2023-05-25T00:32:01Z","abstract_excerpt":"For each partition of the positive integer $n= \\ell +\\sum_{j=1}^\\ell d_j$, where $\\ell\\ge 1$ and $d_j \\ge 0$ are integers, we construct a continuous $(\\ell-1)$-parameter family of explicit complete gradient steady K\\\"ahler--Ricci solitons on $\\mathbb{C}^n$ admitting a hamiltonian $2$-form of order $\\ell$ and symmetry group ${\\rm U}(d_1+ 1) \\times \\cdots \\times {\\rm U}(d_{\\ell} + 1)$. For $\\ell=1, \\, d_1=n-1$ we obtain Cao's example [17] whereas for other partitions the metrics are new. Furthermore, when $n=2, \\, \\ell=2, \\, d_1=d_2=0$ we obtain complete gradient steady K\\\"ahler--Ricci solitons "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.15626","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.15626/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}