Three-fold divisorial extremal neighborhoods over cE7 and cE6 compound duval singularities

Abstract

Let P ∈ Γ ⊂ X be the germ of a Gorenstein three-fold singularity and Γ a smooth curve through it such that the general hyperplane section S of X containing Γ is DuVal of type E6 or E7. In this paper we obtain criteria for the existence of a terminal divisorial extremal neighborhood C ⊂ Y →f X ∋ P contracting an irreducible divisor E onto Γ and classify all such neighborhoods. © 2010 World Scientific Publishing Company.