Singular cubic fourfolds containing a plane

Details Singular cubic fourfolds containing a plane Singular cubic fourfolds containing a plane

2004-04-25

arxiv.org/abs/math/0404448v3

Mathematics

Algebraic Geometry

19 pages. Exposition improved but no new results added to the previous version. Final version to appear in Le Matematiche

Scientific paper

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.

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