ON THOMAE FORMULAS FOR Z3 CURVES
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概要
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In this paper, we give an elementary proof of Thomae formula for Z3 curves. Let C(λ) be a cyclic triple covering parameterized by the set λ of its branch points. We explicitly give the zero divisors of the pullbacks θm(P) of theta functions with some characteristics m under the Abel-Jacobi map from C(λ) to its Jacobian. We take a symplectic basis for the homology group of C(λ) so that we can see the action of a covering transformation ρ on θm(P).
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