On cyclic trigonal Riemann surfaces. I
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- by Robert D. M. Accola PDF
- Trans. Amer. Math. Soc. 283 (1984), 423-449 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 283 (1984), 423-449
- MSC: Primary 14H30; Secondary 14H40, 14H45, 30F35
- DOI: https://doi.org/10.1090/S0002-9947-1984-0737877-1
- MathSciNet review: 737877