{"paper":{"title":"Theta Functions and Adiabatic Curvature on a Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ching-Hao Chang, I-Hsun Tsai, Jih-Hsin Cheng","submitted_at":"2019-05-16T06:37:51Z","abstract_excerpt":"Let $M$ be a complex torus, $L_{\\hat\\mu}\\to M$ be positive line bundles parametrized by $\\hat \\mu\\in {\\rm Pic}^0(M)$, and $E\\to {\\rm Pic}^0(M)$ be a vector bundle with $E|_{\\hat\\mu}\\cong H^0(M, L_{\\hat \\mu})$. We endow the total family $\\{L_{\\hat\\mu}\\}_{\\hat\\mu}$ with a Hermitian metric that induces the $L^2$-metric on $H^0(M, L_{\\hat \\mu})$ hence on $E$. By using theta functions $\\{\\theta_m\\}_{m}$ on $M\\times M$ as a family of functions on the first factor $M$ with parameters in the second factor $M$, our computation of the full curvature tensor $\\Theta_E$ of $E$ with respect to this $L^2$-me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06555","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"}