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arXiv · 0812.3014

On the classification of degree 1 elliptic threefolds with constant $j$-invariant

Remke Kloosterman
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Abstract

We describe the possible Mordell-Weil groups for degree 1 elliptic threefold with rational base and constant $j$-invariant. Moreover, we classify all such elliptic threefolds if the $j$-invariant is nonzero. We can use this classification to describe a class of singular hypersurfaces in $\Ps(2,3,1,1,1)$ that admit no variation of Hodge structure.

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Remke Kloosterman. 2008-12-16. On the classification of degree 1 elliptic threefolds with constant $j$-invariant. https://doi.org/10.1215/ijm/1369841784

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