Singular cubic fourfolds containing a plane
Algebraic Geometry
2011-09-13 v3
Abstract
In this paper we consider cubic 4-folds containing a plane whose discriminant curve is a reduced nodal plane sextic. In particular, we describe the singular points of such cubic 4-folds and we give an estimate of the rank of the free abelian group generated by the equivalence classes of the algebraic cycles of codimension 2. Moreover, we describe some conditions on the geometry of the plane sextics so that all the associated cubic 4-folds are singular and we construct a family of smooth rational cubic 4-folds whose discriminant curve is reduced but reducible.
Cite
@article{arxiv.math/0404448,
title = {Singular cubic fourfolds containing a plane},
author = {Paolo Stellari},
journal= {arXiv preprint arXiv:math/0404448},
year = {2011}
}
Comments
19 pages. Exposition improved but no new results added to the previous version. Final version to appear in Le Matematiche