d-gonality of modular curves and bounding torsions

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We study the problem of $d$-gonality of the modular curve $X_0(N)$. As a result, we can give an upperbound of the level $N$ by means of $d$. This generalizes Ogg's result on hyperelliptic modular curves ($d = 2$). As a corollary of this result, we prove an analogue of the strong Uniform Boundedness Conjecture for elliptic curves defined over the function fields of curves. If a base curve is $d$-gonal, we can bound orders of torsions of Mordell-Weil groups in terms of $d$ uniformly.
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Algebraic Geometry, 14G05 (Primary) 11G05, 14H52 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/150129

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/alg-geom/9603024
 http://arxiv.org/abs/alg-geom/9603024

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arXiv