Trisecant flops, their associated \(K3\) surfaces and the rationality of some cubic fourfolds

DOI10.4171/JEMS/1248zbMATH Open1521.14032arXiv1909.01263MaRDI QIDQ6172681

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Publication date: 20 July 2023

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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.

Full work available at URL: https://arxiv.org/abs/1909.01263

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