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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Chern-Simons invariant and Deligne-Riemann-Roch isomorphism
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by Takashi Ichikawa PDF
Trans. Amer. Math. Soc. 374 (2021), 2987-3005 Request permission


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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Additional Information
  • Takashi Ichikawa
  • Affiliation: Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan
  • MR Author ID: 253584
  • Email:
  • Received by editor(s): May 27, 2020
  • Received by editor(s) in revised form: September 9, 2020
  • Published electronically: February 8, 2021
  • © Copyright 2021 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 2987-3005
  • MSC (2020): Primary 14C40, 58J28; Secondary 14H10, 14H15
  • DOI:
  • MathSciNet review: 4223040