English

On cubic elliptic varieties

Algebraic Geometry 2013-05-16 v1

Abstract

Let X->P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.

Keywords

Cite

@article{arxiv.1305.3340,
  title  = {On cubic elliptic varieties},
  author = {Juergen Hausen and Antonio Laface and Andrea Luigi Tironi and Luca Ugaglia},
  journal= {arXiv preprint arXiv:1305.3340},
  year   = {2013}
}

Comments

20 pages LaTeX

R2 v1 2026-06-22T00:16:40.654Z