Relating derived equivalences for simplices of higher-dimensional flops

Abstract

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.