Sections on certain j=0 elliptic surfaces

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Using some theory of (rational) elliptic surfaces plus elementary properties of a Mordell-Weil group regarded as module over the endomorphism ring of a (CM) elliptic curve, we present examples of such surfaces with j-invariant zero. In particular, a K3 example is given with the maximal possible rank 18, plus that many explicit independent sections on it. Several other high rank cases are discussed; for instance Shioda's example with rank 68.

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Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/79519

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9911274
 http://arxiv.org/abs/math/9911274

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arXiv