Henry Pinkham

Degeneration of surfaces with trivial canonical bundle

The object of this note is to prove the theorem stated below. The main idea of the proof, and much of the detail, are already to be found in V. I. Kulikovs important paper [K]. Our contribution to the proof, and the differences with Kulikovs paper are discussed later in this introduction. THEOREM. Let wl: X -> D be a semistable degeneration of surfaces such that:

On a result of Riemenschneider

O. Riemenschneider has recently exhibited a class of normal 2-dimensional analytic singularities for which some deformations of the minimal resolution cannot be blown down to deformations of the singularity. In this note we identify the obstructions to doing so, using algebraic techniques introduced by Schlessinger and the author.