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

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

2008-12-16

arxiv.org/abs/0812.3014v2

Mathematics

Algebraic Geometry

A new proof for Proposition 3.5 is provided; several minor changes

Scientific paper

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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