BROWN, G. and REID, M., 2013. Diptych varieties, I. Proceedings of the London Mathematical Society, 107 (6), pp. 1353 - 1394.
We present a new class of affine Gorenstein 6-folds obtained by smoothing the 1-dimensional
singular locus of a reducible affine toric surface; their existence is established using explicit
methods in toric geometry and serial use of Kustin–Miller Gorenstein unprojection. These
varieties have applications as key varieties in constructing other varieties, including local models
of Mori flips of Type A.
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This work was partially funded by Korean Government WCU Grant R33-2008-000-10101-0.