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 Cd, with d = 14, 26, 38, and 42 and some birational models of K3 surfaces of degree d contained in well known rational Fano fourfolds.

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

Francesco Russo
;
Giovanni Staglianò
2023-01-01

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 Cd, with d = 14, 26, 38, and 42 and some birational models of K3 surfaces of degree d contained in well known rational Fano fourfolds.
2023
Rationality of cubic fourfolds
Flops
Mori Theory
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/518423
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