Blowing Ups of 3-dimensional Terminal Singularities

Abstract

We study the blowing up π : X -> X of a 3-dimensional terminal singularity X of index m > 2 such that the exceptional locus of π consists of a prime divisor E with discrepancy 1/m. A complete classification of such blowing ups is given and it is proved that these correspond to weighted blow ups by a certain kind of maximal weights except for the case where X is of type (cD/2). We shall treat the (cD/2) case later. These also give examples of contractions of extremal rays which contract a divisor to a point.