Three dimensional divisorial extremal neighborhoods

Abstract

Revised version. Proper credits added. In this paper we study divisorial extremal neighborhoods f:Y-->X, such that X is a cAn type three dimensional terminal singularity, and C=f(E) is a smooth curve, where E is the f-exceptional divisor. We view a divisorial extremal neighborhood as a one-parameter smoothing of certain surface singularities, and based on this we give a classification of such neighborhoods.