{"paper":{"title":"Plurisubharmonically separable complex manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Evgeny A. Poletsky, Nikolay Shcherbina","submitted_at":"2017-12-06T02:04:49Z","abstract_excerpt":"Let $M$ be a complex manifold and $PSH^{cb}(M)$ be the space of bounded continuous plurisubharmonic functions on $M$. In this paper we study when functions from $PSH^{cb}(M)$ separate points. Our main results show that this property is equivalent to each of the following properties of $M$:\n  (1) the core of $M$ is empty.\n  (2) for every $w_0\\in M$ there is a continuous plurisubharmonic function $u$ with the logarithmic singularity at $w_0$.\n  Moreover, the core of $M$ is the disjoint union of 1-pseudoconcave in the sense of Rothstein sets $E_j$ with the following Liouville property: every func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02005","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"}