English

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

Algebraic Geometry 2024-10-21 v2

Abstract

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

Keywords

Cite

@article{arxiv.0812.3014,
  title  = {On the classification of degree 1 elliptic threefolds with constant $j$-invariant},
  author = {Remke Kloosterman},
  journal= {arXiv preprint arXiv:0812.3014},
  year   = {2024}
}

Comments

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