VOL. 88 | 2023 Relating derived equivalences for simplices of higher-dimensional flops
Will Donovan

Editor(s) Yukari Ito, Akira Ishii, Osamu Iyama

Adv. Stud. Pure Math., 2023: 305-330 (2023) DOI: 10.2969/aspm/08810305


I study a sequence of singularities in dimension 4 and above, each given by a cone of rank 1 tensors of a certain signature, which have crepant resolutions whose exceptional loci are isomorphic to cartesian powers of the projective line. In each dimension $n$, these resolutions naturally correspond to vertices of an $(n - 2)$-simplex, and flops between them correspond to edges of the simplex. I show that each face of the simplex may then be associated to a certain relation between flop functors.


Published: 1 January 2023
First available in Project Euclid: 8 May 2023

Digital Object Identifier: 10.2969/aspm/08810305

Primary: 14F08
Secondary: 14J32 , 18G80

Keywords: birational geometry , Calabi–Yau manifolds , Crepant resolutions , derived category , derived equivalence , flops , simplices , tensors

Rights: Copyright © 2023 Mathematical Society of Japan


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