  We present a hypersurface singularity in positive characteristic which is
defined by a purely inseparable power series, and a sequence of point blowups
so that, after applying the blowups to the singularity, the same type of
singularity reappears after the last blowup, with just certain exponents of the
defining power series shifted upwards. The construction hence yields a cycle.
Iterating this cycle leads to an infinite increase of the residual order of the
defining power series. This disproves a theorem claimed by Moh about the
stability of the residual order under sequences of blowups. It is not a
counter-example to the resolution in positive characteristic since larger
centers are also permissible and prevent the phenomenon from happening.

Algebraic Geometry