Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rationality, universal generation and the integral Hodge conjecture   We use the universal generation of algebraic cycles to relate (stable)
rationality to the integral Hodge conjecture. We show that the Chow group of
1-cycles on a cubic hypersurface is universally generated by lines.
Applications are mainly in cubic hypersurfaces of low dimensions. For example,
we show that if a generic cubic fourfold is stably rational then the
Beauville--Bogomolov form on its variety of lines, viewed as an integral Hodge
class on the self product of its variety of lines, is algebraic. In dimension
$3$ and $5$, we relate stable rationality with the geometry of the associated
intermediate Jacobian.

18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas