Derived categories of quartic double fivefolds

2024/03/20 by Raymond Cheng, Cheng, Raymond, Perry Alexander +3
Mathematics · #14D06 (secondary) #14E08 (primary) #14F08 #14M20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.13463

openalex publication_date 2024/03/20 · openalex created_date 2025/05/16 · openalex updated_date 2026/08/03

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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