{"paper":{"title":"On piecewise pluriharmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Boris Kazarnovskii","submitted_at":"2012-06-17T10:24:05Z","abstract_excerpt":"We extend some results on piecewise linear functions on $\\C^n$ to piecewise pluriharmonic functions on any complex manifold.\n  We construct a ring generated by currents $h$ and $dd^ch$, where $\\{h\\}$ is a finite set of piecewise pluriharmonic functions.\n  We prove that, with some restrictions on the set $\\{h\\}$, the map $\\{h\\mapsto dd^ch,\\ dd^ch\\mapsto0\\}$ can be continued to the derivation on the ring.\n  As a corollary, the current $dd^cg_1\\wedge...\\wedge dd^cg_k$ depends on the product of piecewise pluriharmonic functions $g_1,...,g_k$ only."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3741","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"}