Idealistic exponents: Tangent cone, ridge, characteristic polyhedra

Abstract

We study Hironaka's idealistic exponents over Spec (Z). We give an idealistic interpretation of the tangent cone, the directrix, and the ridge. The main purpose is to introduce the notion of characteristic polyhedra of idealistic exponents and deduce from them intrinsic data on the idealistic exponent. (C) 2020 Elsevier Inc. All rights reserved.