Chern-Simons invariant and Deligne-Riemann-Roch isomorphism

Ichikawa, Takashi

doi:10.1090/tran/8320

Chern-Simons invariant and Deligne-Riemann-Roch isomorphism
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Abstract:

Using the arithmetic Schottky uniformization theory, we show the arithmeticity of $PSL_{2}({\mathbb C})$ 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.

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