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 P(2, 3, 1, 1, 1) that admit no variation of Hodge structure (Remark 9.3).
Citation
Remke Kloosterman. "On the classification of degree 1 elliptic threefolds with constant j-invariant." Illinois J. Math. 55 (3) 771 - 803, Fall 2011. https://doi.org/10.1215/ijm/1369841784
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