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MR965750 (89i:32054) 32J05 (11F46 11F75 11G18 14H15)
Lee, Ronnie; Weintraub, Steven H. Moduli spaces of Riemann surfaces of genus two with level structures. I. Trans. Amer. Math. Soc. 310 (1988), no. 1, 217–237.
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