Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two rationality conjectures for cubic fourfolds   Motivated by the question of rationality of cubic fourfolds, we show that a
cubic X has an associated K3 surface in the sense of Hassett if and only if the
variety F of lines on X is birational to a moduli space of sheaves on a K3
surface, but that having F birational to Hilb^2(K3) is more restrictive. We
compare the loci in the moduli space of cubics where each condition is
satisfied.

37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc