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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On cyclic trigonal Riemann surfaces. I


Author: Robert D. M. Accola
Journal: Trans. Amer. Math. Soc. 283 (1984), 423-449
MSC: Primary 14H30; Secondary 14H40, 14H45, 30F35
MathSciNet review: 737877
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Abstract: Definition. Call the Riemann surfaces for the equation $ {y^3} = P(x)$ cyclic trigonal. For one case of genus $ 4$ ($ 2$ distinct $ g_3^1$'s) and all genera greater than $ 4$, cyclic trigonal Riemann surfaces are characterized by the vanishing properties of the theta function at certain $ (1/6)$-periods of the Jacobian. Also for trigonal Riemann surfaces of genera $ 5$, $ 6$, and $ 7$, homogeneous theta relations are derived using the fact that Prym varieties for trigonal Riemann surfaces are Jacobians.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0737877-1
PII: S 0002-9947(1984)0737877-1
Keywords: Riemann surfaces, automorphisms, algebraic curve, Jacobian, Prym variety
Article copyright: © Copyright 1984 American Mathematical Society