Semistable 3-fold Flips

1 Introduction. In this short note, I will give a proof of the existence of semistable 3-fold flips, which does not use the classification of log terminal (i.e., quotient) surface singularities. This permits us to avoid a calculation, which is a sort of logical bottleneck in all the existing approaches to semistable 3-fold flips ([Ka1 pg. 158–159], [Sh pg. 386–389], [Ka3 pg. 483–486]), however different they may look. The message is that Shokurov's main reduction step, as refined in [FA, Ch. 18], can be used profitably in the semistable case also. My main motivation was to develop an approach to semistable flips that would have some fighting chances in dimension 4, and the present paper is a first (small) step in that direction. We always work over an algebraically closed field of characteristic zero.