Reid's recipe and derived categories
Timothy Logvinenko

TL;DR
This paper proves two conjectures linking the geometric McKay correspondence with Reid's recipe for certain singularities, using derived categories and toric combinatorics to deepen understanding of the correspondence.
Contribution
It provides a categorification of Reid's recipe by connecting derived category techniques with toric combinatorics in the context of the McKay correspondence.
Findings
Proved two conjectures relating McKay correspondence and Reid's recipe
Established a link between Fourier-Mukai transforms and toric combinatorics
Enhanced understanding of singularities in SL3(C) quotients
Abstract
We prove two existing conjectures which describe the geometrical McKay correspondence for a finite abelian G in SL3(C) such that C^3/G has a single isolated singularity. We do it by studying the relation between the derived category mechanics of computing a certain Fourier-Mukai transform and a piece of toric combinatorics known as `Reid's recipe', effectively providing a categorification of the latter.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology
