{"paper":{"title":"The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"George Marinescu, Xiaonan Ma","submitted_at":"2005-11-16T08:49:04Z","abstract_excerpt":"We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin-c Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending the paper \" On the asymptotic expansion of Bergman kernel \" (math.DG/0404494) of Dai-Liu-Ma. We compute the second coefficient b_1 in the asymptotic expansion using the method of our paper \"Generalized Bergman kernels on symplectic manifolds\" (math.DG/0411559)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511395","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"}