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.
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