We consider single-valued meromorphic functions and differentials on finite Riemann surfaces. We construct elementary q-differentials of all types. We find the dimension of two important quotient spaces of Abelian q-differentials, in particular, the first holomorphic de Rham cohomology group of 1-differentials. For these quotient spaces we construct bases that locally holomorphically depend on the moduli of the Riemann surfaces. Bibliography: 6 titles.
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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 14, No. 3, 2014, pp. 50–61.
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Kazantseva, A.A. Single-Valued q-Differentials on a Variable Finite Riemann Surface. J Math Sci 213, 857–867 (2016). https://doi.org/10.1007/s10958-016-2747-8
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DOI: https://doi.org/10.1007/s10958-016-2747-8