The Gonality Of Riemann Surfaces Under Projections By Normal Coverings
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2011
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Elsevier Science
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Bujalance García, E., Etayo Gordejuela, J. J., Gamboa Mutuberria, J. M. & Gromadzki, G. «The Gonality of Riemann Surfaces under Projections by Normal Coverings». Journal of Pure and Applied Algebra, vol. 215, n.o 5, mayo de 2011, pp. 983-88. DOI.org (Crossref), https://doi.org/10.1016/j.jpaa.2010.07.004.
Abstract
A compact Riemann surface X of genus g ≥ 2 which can be realized as a q-fold, normal covering of a compact Riemann surface of genus p is said to be (q, p)-gonal.
In particular the notion of (2, p)-gonality coincides with p-hyperellipticity and (q, 0)-gonality coincides with ordinary q-gonality.
Here we completely determine the relationship between the
gonalities of X and Y for an N-fold normal covering X → Y between compact Riemann surfaces X and Y.
As a consequence we obtain classical results due to Maclachlan (1971) [5] and Martens (1977) [6].