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arXiv · 2403.13463

Derived categories of quartic double fivefolds

Raymond Cheng·Alexander Perry·Xiaolei Zhao
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Abstract

We construct singular quartic double fivefolds whose Kuznetsov component admits a crepant categorical resolution of singularities by a twisted Calabi--Yau threefold. We also construct rational specializations of these fivefolds where such a resolution exists without a twist. This confirms an instance of a higher-dimensional version of Kuznetsov's rationality conjecture, and of a noncommutative version of Reid's fantasy on the connectedness of the moduli of Calabi--Yau threefolds.

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Raymond Cheng, Alexander Perry, Xiaolei Zhao. 2024-03-20. Derived categories of quartic double fivefolds. https://doi.org/10.1093/imrn/rnaf119

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