{"paper":{"title":"Szeg\\\"o kernel asymptotics for high power of CR line bundles and Kodaira embedding theorems on CR manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Chin-Yu Hsiao","submitted_at":"2014-01-26T13:33:37Z","abstract_excerpt":"Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $n\\geqslant2$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Given $q\\in\\set{0,1,\\ldots,n-1}$, let $\\Box^{(q)}_{b,k}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$ forms with values in $L^k$. For $\\lambda\\geq0$, let $\\Pi^{(q)}_{k,\\leq\\lambda}:=E((-\\infty,\\lambda])$, where $E$ denotes the spectral measure of $\\Box^{(q)}_{b,k}$. In this work, we prove that $\\Pi^{(q)}_{k,\\leq k^{-N_0}}F^*_k$, $F_k\\Pi^{(q)}_{k,\\leq k^{-N_0}}F^*_k$, $N_0\\geq1$, admit asymptotic ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6647","kind":"arxiv","version":4},"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"}