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arXiv · 1305.3340

On cubic elliptic varieties

Juergen Hausen·Antonio Laface·Andrea Luigi Tironi·Luca Ugaglia
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Abstract

Let X->P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.

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Juergen Hausen, Antonio Laface, Andrea Luigi Tironi, Luca Ugaglia. 2013-05-15. On cubic elliptic varieties. https://arxiv.org/abs/1305.3340

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