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On spaces associated with invariant divisors on Galois covers of Riemann surfaces and their applications

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Abstract

Let f : X → S be a Galois cover of Riemann surfaces, with Galois group G. I. this paper we analyze the G-invariant divisors on X, and their associated spaces of meromorphic functions, differentials, and q-differentials. We generalize the trace formula for non-trivial elements of G on q-differentials, as well as the Chevalley–Weil Formula. When G is Abelian or when the genus of S is 0 we prove additional results, and we also determine the non-special G-invariant divisors when both conditions are satisfied.

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Authors and Affiliations

  1. Finance Department, School of Business, University of Connecticut, 2100 Hillside road, Storrs, CT, 06268, USA

    Yaacov Kopeliovich

  2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem Edmund Safra Campus, Jerusalem, 91904, Israel

    Shaul Zemel

Authors
  1. Yaacov Kopeliovich
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  2. Shaul Zemel
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Correspondence to Shaul Zemel.

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Kopeliovich, Y., Zemel, S. On spaces associated with invariant divisors on Galois covers of Riemann surfaces and their applications. Isr. J. Math. 234, 393–450 (2019). https://doi.org/10.1007/s11856-019-1946-7

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  • DOI: https://doi.org/10.1007/s11856-019-1946-7

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