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). 2013 © University of Illinois.
On the classification of degree 1 elliptic threefolds with constant j-invariant
KLOOSTERMAN, REMKE NANNE
2011
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). 2013 © University of Illinois.
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