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The spaces of meromorphic Prym differentials on a finite Riemann surface

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Abstract

In the previous articles the second author started constructing a general theory of multiplicative functions and Prym differentials on a compact Riemann surface for arbitrary characters. Function theory on compact Riemann surfaces differs substantially from that on finite Riemann surfaces. In this article we start constructing a general function theory on variable finite Riemann surfaces for multiplicative meromorphic functions and differentials. We construct the forms of all elementary Prym differentials for arbitrary characters and find the dimensions of, and also construct explicit bases for, two important quotient spaces of Prym differentials. This yields the dimension of and a basis for the first holomorphic de Rham cohomology group of Prym differentials for arbitrary characters.

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Author information

Authors and Affiliations

  1. Gorno-Altaĭsk State University, Gorno-Altaĭsk, Russia

    A. A. Kazantseva

  2. Kemerovo State University, Kemerovo, Russia

    V. V. Chueshev

Authors
  1. A. A. Kazantseva
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  2. V. V. Chueshev
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Corresponding author

Correspondence to A. A. Kazantseva.

Additional information

Original Russian Text Copyright © 2012 Kazantseva A. A. and Chueshev V. V.

The authors were supported by the Russian Federal Agency for Education (Grant 2.1.1.3707), the Federal Target Program (Contract 02.740.11.0457), the Russian Foundation for Basic Research (Grant 09-01-00255), and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh 7347.2010.1).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 1, pp. 89–106, January–February, 2012.

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Kazantseva, A.A., Chueshev, V.V. The spaces of meromorphic Prym differentials on a finite Riemann surface. Sib Math J 53, 72–86 (2012). https://doi.org/10.1134/S0037446612010065

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  • DOI: https://doi.org/10.1134/S0037446612010065

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