{"paper":{"title":"Bergman metrics and geodesics in the space of K\\\"{a}hler metrics on principally polarized Abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Renjie Feng","submitted_at":"2009-10-13T06:03:51Z","abstract_excerpt":"It's well-known in \\kahler geometry that the infinite dimensional symmetric space $\\hcal$ of smooth \\kahler metrics in a fixed \\kahler class on a polarized \\kahler manifold is well approximated by finite dimensional submanifolds $\\bcal_k \\subset \\hcal$ of Bergman metrics of height $k$. Then it's natural to ask whether geodesics in $\\hcal$ can be approximated by Bergman geodesics in $\\bcal_k$. For any polarized \\kahler manifold, the approximation is in the $C^0$ topology. While Song-Zelditch proved the $C^2$ convergence for the torus-invariant metrics over toric varieties. In this article, we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2311","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"}