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Chern-Simons invariant and Deligne-Riemann-Roch isomorphism
Transactions of the American Mathematical Society ( IF 1.2 ) Pub Date : 2021-02-08 , DOI: 10.1090/tran/8320 Takashi Ichikawa
Transactions of the American Mathematical Society ( IF 1.2 ) Pub Date : 2021-02-08 , DOI: 10.1090/tran/8320 Takashi Ichikawa
Abstract:Using the arithmetic Schottky uniformization theory, we show the arithmeticity of 
Chern-Simons invariant. In terms of this invariant, we give an explicit formula of the Deligne-Riemann-Roch isomorphism as the Zograf-McIntyre-Takhtajan infinite product for families of algebraic curves. Applying this formula to the Liouville theory, we determine the unknown constant which appears in the holomorphic factorization formula of determinants of Laplacians on Riemann surfaces.
中文翻译：
Chern-Simons不变和Deligne-Riemann-Roch同构
摘要：利用算术肖特基均匀化理论，证明了Chern-Simons不变量的算术性。根据该不变性，我们给出了代数曲线族的一个显式的Deligne-Riemann-Roch同构公式，作为Zograf-McIntyre-Takhtajan无限积。将此公式应用于Liouville理论，我们确定了未知常数，该常数出现在Riemann曲面上Laplacians行列式的全纯因式分解公式中。
更新日期：2021-03-02
Chern-Simons invariant. In terms of this invariant, we give an explicit formula of the Deligne-Riemann-Roch isomorphism as the Zograf-McIntyre-Takhtajan infinite product for families of algebraic curves. Applying this formula to the Liouville theory, we determine the unknown constant which appears in the holomorphic factorization formula of determinants of Laplacians on Riemann surfaces. 中文翻译：
Chern-Simons不变和Deligne-Riemann-Roch同构
摘要：利用算术肖特基均匀化理论，证明了Chern-Simons不变量的算术性。根据该不变性，我们给出了代数曲线族的一个显式的Deligne-Riemann-Roch同构公式，作为Zograf-McIntyre-Takhtajan无限积。将此公式应用于Liouville理论，我们确定了未知常数，该常数出现在Riemann曲面上Laplacians行列式的全纯因式分解公式中。
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