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Tropical degenerations and stable rationality

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arxiv 1911.06138 v4 pith:CBJ3KXLP submitted 2019-11-14 math.AG

Johannes Nicaise , John Christian Ottem This is my paper · ORCID
classification math.AG
keywords completeintersectionsirrationalrationalitystablestablytropicalauthor
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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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  1. Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds

    math.AG 2019-09 conditional novelty 8.0 of 10

    Every cubic fourfold of discriminant 42 is rational, established through a new trisecant-flop construction from the minimal model program.

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