Dennis Clark

Bend and Break


Regular listeners will recall from last week that the Mori program for classification of varieties over C depends in part on finding, for any variety X, a birationally equivalent variety X_min having nef canonical divisor.  One of the important methods for this is contracting rational curves; to do this, we must first find some rational curves to contract.  Bend and break is Mori's trick for achieving this using a reduction to characteristic p.