Diptych varieties. I

Abstract

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.Comment: 50 pages. The webpage at www-staff.lboro.ac.uk/~magdb/aflip.html contains links to auxiliary materia