{"paper":{"title":"Pluripolar hulls and convergence sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daowei Ma, Juan Chen","submitted_at":"2017-10-24T15:07:51Z","abstract_excerpt":"The pluripolar hull of a pluripolar set E in $\\mathbb{P}^n$ is the intersection of all complete pluripolar sets in $\\mathbb{P}^n$ that contain $E$. We prove that the pluripolar hull of each compact pluripolar set in $\\mathbb{P}^n$ is $F_\\sigma$. The convergence set of a divergent formal power series $f(z_{0}, \\dots,z_{n})$ is the set of all \"directions\" $\\xi \\in\\mathbb{P}^{n}$ along which $f$ is convergent. We prove that the union of the pluripolar hulls of a countable collection of compact pluripolar sets in $\\mathbb{P}^n$ is the convergence set of some divergent series $f$. The convergence s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08827","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"}