{"paper":{"title":"(Volume) Density Property of a family of complex manifolds including the Koras-Russell Cubic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Matthias Leuenberger","submitted_at":"2015-07-14T13:23:44Z","abstract_excerpt":"We present modified versions of existing criteria for the density property and the volume density property of complex manifolds. We apply this methods to show the (volume) density property for a family of manifolds given by $x^2y=a(\\bar z) + xb(\\bar z)$ with $\\bar z =(z_0,\\ldots,z_n)\\in\\mathbb{C}^{n+1}$ and volume form $\\mathrm{d} x/x^2\\wedge \\mathrm{d} z_0\\wedge\\ldots\\wedge\\mathrm{d} z_n$. The key step is showing that in certain cases transitivity of the action of (volume preserving) holomorphic automorphisms implies the (volume) density property, and then giving sufficient conditions for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03842","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"}