Every cubic fourfold of discriminant 42 is rational, established through a new trisecant-flop construction from the minimal model program.
Tropical degenerations and stable rationality
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abstract
We use the motivic obstruction to stable rationality introduced by Shinder and the first-named author to establish several new classes of stably irrational hypersurfaces and complete intersections. In particular, we show that very general quartic fivefolds and complete intersections of a quadric and a cubic in $\mathbb P^6$ are stably irrational. An important new ingredient is the use of tropical degeneration techniques.
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Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds
Every cubic fourfold of discriminant 42 is rational, established through a new trisecant-flop construction from the minimal model program.