{"paper":{"title":"Scaling asymptotics of heat kernels of line bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"George Marinescu, Steve Zelditch, Xiaonan Ma","submitted_at":"2014-06-01T20:50:00Z","abstract_excerpt":"We consider a general Hermitian holomorphic line bundle $L$ on a compact complex manifold $M$ and let ${\\Box}^q_p$ be the Kodaira Laplacian on $(0,q)$ forms with values in $L^p$. The main result is a complete asymptotic expansion for the semi-classically scaled heat kernel $\\exp(-u{\\Box}^q_p/p)(x,x)$ along the diagonal. It is a generalization of the Bergman/Szeg\\\"o kernel asymptotics in the case of a positive line bundle, but no positivity is assumed. We give two proofs, one based on the Hadamard parametrix for the heat kernel on a principal bundle and the second based on the analytic localiza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0201","kind":"arxiv","version":1},"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"}