Papers › Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds
Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds
Francesco Russo, Giovanni Staglianò
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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 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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