https://scholars.lib.ntu.edu.tw/handle/123456789/625096
Title: | Theta Functions and Adiabatic Curvature on an Elliptic Curve | Authors: | Chang C.-H Cheng J.-H I-HSUN TSAI |
Keywords: | Connection; Curvature; Poincaré line bundle; Theta functions | Issue Date: | 2022 | Journal Volume: | 32 | Journal Issue: | 3 | Source: | Journal of Geometric Analysis | Abstract: | Let M be a complex torus, Lμ^→ M be positive line bundles parametrized by μ^ ∈ Pic (M) , and E→ Pic (M) be a vector bundle with E| μ^≅ H(M, Lμ^). We endow the total family {Lμ^}μ^ with a Hermitian metric that induces the L2-metric on H(M, Lμ^) hence on E. Using theta functions {θm}m on M× 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 Θ E of E with respect to this L2-metric shows that Θ E is essentially an identity matrix multiplied by a constant 2-form, which yields in particular the adiabatic curvature c1(E). After a natural base change M→ M^ so that E× M^M: = E′, we obtain that E′ splits holomorphically into a direct sum of line bundles each of which is isomorphic to Lμ^=0∗. © 2021, Mathematica Josephina, Inc. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85122954169&doi=10.1007%2fs12220-021-00774-2&partnerID=40&md5=704c79c8b5fe17d6f32b4abf9d6eaa01 https://scholars.lib.ntu.edu.tw/handle/123456789/625096 |
ISSN: | 10506926 | DOI: | 10.1007/s12220-021-00774-2 |
Appears in Collections: | 數學系 |
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