Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On relations among 1-cycles on cubic hypersurfaces   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.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio