Seventeen Obstacles for Resolution of Singularities

This is the first of a series of papers related to resolution of singularities. We present here examples which explain why many arguments and proofs work in special situations, say small dimension or zero characteristic, but fail in general. This exhibits in particular the delicacy of resolution of singularity for arbitrary excellent schemes. The examples were originally assembled for the author’s personal records. They might be of some interest to a larger audience, especially to readers for whom the flavour of resolution of singularities is concealed by technique.