Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trisecant Flops, their associated K3 surfaces and the rationality of
  some Fano fourfolds   We provide a new construction of rationality for cubic fourfolds via Mori's
theory and the minimal model program. As an application, we present the
solution of the Kuznetsov's conjecture for $d=42$ (the first open case). Our
methods also show an explicit connection between the rationality of cubic
fourfolds belonging to the first four admissible families $\mathcal C_d$, with
$d=14,26,38$, and $42$ and some birational models of minimal K3 surfaces of
degree $d$ contained in well known rational Fano fourfolds.

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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex