Threefold extremal contractions of type (IIA). I

摘要

Let (X, C) be a germ of a threefold X with terminal singularities along an irreducible reduced complete curve C with a contraction f : (X, C) -> (Z, o) such that C - f(-1) (o) red and -K-X is ample. Assume that (X, C) contains a point of type (IIA) and that a general member H is an element of vertical bar O-X vertical bar containing C is normal. We classify such germs in terms of H.