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arXiv · 1909.01263

Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds

Francesco Russo·Giovanni Staglianò
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Abstract

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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Francesco Russo, Giovanni Staglianò. 2019-09-03. Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds. https://arxiv.org/abs/1909.01263

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