Bielliptic Curves and Symmetric Products
Copyright policy )Bielliptic Curves and Symmetric Products
We show that the twofold symmetric product of a nonhyperelliptic, nonbielliptic curve does not contain any elliptic curves. Applying a theorem of Faltings, we conclude that such a curve defined over a number field K K has only finitely many points over all quadratic extensions of K K . We illustrate our theory with the modular curves X 0 ( N ) , X 1 ( N ) , X ( N ) {X_0}(N),{X_1}(N),X(N) .
Curves of arbitrary genus or genus \(\ne 1\) over global fields, quadratic point, hyperelliptic curve, Algebraic functions and function fields in algebraic geometry, modular curves, Arithmetic aspects of modular and Shimura varieties, bielliptic curve
Curves of arbitrary genus or genus \(\ne 1\) over global fields, quadratic point, hyperelliptic curve, Algebraic functions and function fields in algebraic geometry, modular curves, Arithmetic aspects of modular and Shimura varieties, bielliptic curve
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