{"paper":{"title":"On the polynomial convexity of the union of more than two totally-real planes in C^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sushil Gorai","submitted_at":"2011-08-29T16:12:51Z","abstract_excerpt":"In this paper we shall discuss local polynomial convexity at the origin of the union of finitely many totally-real planes through $0 \\in\\mathbb{C}^2$. The planes, say $P_0,..., P_N$, satisfy a mild transversality condition that enables us to view them in Weinstock normal form, i.e. $P_0=\\mathbb{R}^2$ and $P_j=M(A_j):=(A_j+i\\mathbb{I})\\mathbb{R}^2$, $j=1,...,N$, where each $A_j$ is a $2\\times 2$ matrix with real entries. Weinstock has solved the problem completely for N=1 (in fact, for pairs of transverse, maximally totally-real subspaces in $\\mathbb{C}^n\\, \\forall n\\geq 2$). Using a characteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5625","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"}