{"paper":{"title":"A geometric approach to Catlin's boundary systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dmitri Zaitsev","submitted_at":"2017-04-06T12:46:03Z","abstract_excerpt":"For a point $p$ in a smooth real hypersurface $M\\subset\\C^n$, where the Levi form has the nontrivial kernel $K^{10}_p$, we introduce an invariant cubic tensor $\\tau^3_p \\colon \\C T_p \\times K^{10}_p \\times \\overline{K^{10}_p} \\to \\C\\otimes (T_p/H_p)$, which together with Ebenfelt's tensor $\\psi_3$, constitutes the full set of $3$rd order invariants of $M$ at $p$.\n  Next, in addition, assume $M\\subset\\C^n$ to be {\\em (weakly) pseudoconvex}. Then $\\tau^3_p$ must identically vanish. In this case we further define an invariant quartic tensor $\\tau^4_p \\colon \\C T_p \\times \\C T_p\n  \\times K^{10}_p\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01808","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"}