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In this article we give an explicit construction of the moduli space oftrigonal superelliptic curves with level 3 structure. The construction is givenin terms of point sets on the projective line and leads to a closed formula forthe number of connected (and irreducible) components of the moduli space. Theresults of the article generalise the description of the moduli space ofhyperelliptic curves with level 2 structure, due to Dolgachev and Ortland,Runge and Tsuyumine.

Explicit Moduli of Superelliptic Curves with Level Structure