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

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.

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

References in corpus (2)

• Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
• The elliptic threefold y^2=x^3+16s^6+16t^6-32(t^3s^3+t^3+s^3)+16

Cited by in corpus (2)

• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces