3-fold divisorial extremal neighborhoods over cE7 and cE6 Compound DuVal singularities

Abstract

Let X be the germ of a Gorenstein 3-fold singularity and C a smooth curve through it such that the general hyperplane section S of X containing D is DuVal of type E6 or E7. In this paper we obtain criteria for the existence of a terminal divisorial extremal neighborhood f: Y-->X contracting an irreducible divisor E onto C and classify all such neighborhoods.

A section has been added classifying all divisorial extremal neighborhoods f:Y-->X such that if E is the f-exceptional divisor and C=f(E), the general hyperplane section S of X containg C is DuVal of type E6. The previous version classified only the E7 case. 20 pages