Appendix. hironaka’s characteristic polyhedron. notes for novices(b.schober)

Abstract

In this appendix, we discuss some of the ideas behind Hironaka’s characteristic polyhedron. In particular, we present pictures that are often hidden in the background. The goal is to introduce the reader to the notion of Hironaka’s characteristic polyhedron. Existing references often work in the most general setting in order to develop and to prove new interesting results involving the characteristic polyhedron in the greatest possible generality. This has the drawback that one has to handle a heavy load of technicalities, in which a reader, who is inexperienced on the topic, might easily get lost in. While an introduction with all technical details may be found in Cossart et al. (Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes, Lecture Notes in Mathematics, the present monograph, 2013, Chap. 8), we highlight the ideas behind the characteristic polyhedron and behind the notions appearing within its context.