Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Loci of Rational Cubic Fourfolds   In this paper we investigate the divisor $\mathcal C_{14}$ inside the moduli
space of smooth cubic hypersurfaces in $\mathbb P^5$, whose generic element is
a smooth cubic containing a smooth quartic scroll. Using the fact that all
degenerations of quartic scrolls in $\mathbb P^5$ contained in a smooth cubic
hypersurface are surfaces with one apparent double point, we conclude that
every cubic hypersurface belonging to $\mathcal C_{14}$ is rational. As an
application of our results and of the construction of some explicit examples
contained in the Appendix, we also prove that the Pfaffian locus is not open in
$\mathcal C_{14}$.

13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph