Alternative Invariants for the Embedded Resolution of Purely Inseparable Surface Singularities

Abstract: The article investigates the behaviour of the characteristic zero resolution invariant when transcribed suitably to the case of surfaces in positive characteristic. By Moh's jumping phenomenon -- or the occurrence of kangaroo singularities -- one knows that the invariant may increase, thus destroying any induction. We describe in the paper how one can modify in the purely inseparable surface case the invariant by adding a subtle correction term so as to prohibit its occasional increases and to establish the induction argument again.