Terminal 3-fold divisorial contractions of a surface to a curve, I
Abstract
Let C be a smooth curve on an index 1 terminal 3-fold. We investigate the existence of extremal terminal divisorial contractions Y-->X that contract an irreducible surface E to C. We consider cases in respect to the singularities of the general hypersurface section S of X through C. We completely classify such contractions in the case that S has Ai, i < 4 and D2n for any n, type singularities.
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