On relations among 1-cycles on cubic hypersurfaces

Details On relations among 1-cycles on cubic hypersurfaces On relations among 1-cycles on cubic hypersurfaces

2011-02-13

arxiv.org/abs/1102.2550v2

Mathematics

Algebraic Geometry

24 pages. In the theorem realizing intermediate jacobian as Prym-Tjurin variety, we added the assumption that the curve $C$ is

Scientific paper

In this paper we give two explicit relations among 1-cycles modulo rational equivalence on a smooth cubic hypersurfaces $X$. Such a relation is given in terms of a (pair of) curve(s) and its secant lines. As the first application, we reprove Paranjape's theorem that $\mathrm{CH}_1(X)$ is always generated by lines and that it is isomorphic to $\Z$ if the dimension of $X$ is at least 5. Another application is to the intermediate jacobian of a cubic threefold $X$. To be more precise, we show that the intermediate jacobian of $X$ is naturally isomorphic to the Prym-Tjurin variety constructed from the curve parameterizing all lines meeting a given curve on $X$. The incidence correspondences play an important role in this study. We also give a description of the Abel-Jacobi map for 1-cycles in this setting.

Affiliated with

Also associated with

No associations

Rating

On relations among 1-cycles on cubic hypersurfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On relations among 1-cycles on cubic hypersurfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On relations among 1-cycles on cubic hypersurfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-101