Diptych varieties and Mori flips -- Miles Reid

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Our joint work with Gavin Brown constructs affine
    Gorenstein 6-folds with a (CC^*)^4 action, and
    having two different toric 4-folds as sections; they
    can be viewed as 4-parameter deformations of a
    rectangular tent, that is, a reducible affine
    surface consisting of 4 toric components.  The
    combinatorics of the construction depends on 3
    discrete indexes.  These diptych varieties serve as
    key varieties for Mori flips of type A.