Embedded Resolution of Singularities in Rigid Analytic Geometry
نویسنده
چکیده
We give a rigid analytic version of Hironaka’s Embedded Resolution of Singularities over an algebraically closed field of characteristic zero, complete with respect to a non-archimedean norm. This resolution is local with respect to the Grothendieck topology. The proof uses Hironaka’s original result, together with an application of our analytization functor. 0. Introduction and preliminaries.
منابع مشابه
A Multi-dimensional Resolution of Singularities with Applications to Analysis
We formulate a resolution of singularities algorithm for analyzing the zero sets of real-analytic functions in dimensions ≥ 3. Rather than using the celebrated result of Hironaka, the algorithm is modeled on a more explicit and elementary approach used in the contemporary algebraic geometry literature. As an application, we define a new notion of the height of real-analytic functions, compute t...
متن کاملFlattening and Subanalytic Sets in Rigid Analytic Geometry
Let K be an algebraically closed field endowed with a complete nonarchimedean norm with valuation ring R. Let f : Y → X be a map of K-affinoid varieties. In this paper we study the analytic structure of the image f(Y ) ⊂ X; such an image is a typical example of a subanalytic set. We show that the subanalytic sets are precisely the D-semianalytic sets, where D is the truncated division function ...
متن کاملStrengthening the Theorem of Embedded Desingularization
Resolution of singularities is one of the central areas of research in Algebraic Geometry. It is a basic prerequisite for the classification of algebraic varieties up to birational equivalence, since it allows to consider only regular varieties. Hironaka’s monumental work [Hi1] gave a non-constructive, existence proof of resolution of singularities over fields of characteristic zero. Constructi...
متن کاملLOCAL GEOMETRY OF SINGULAR REAL ANALYTICSURFACESDANIEL GRIESERAbstract
Let V R N be a compact real analytic surface with isolated singularities, and assume its smooth part V0 is equipped with a Riemannian metric that is induced from some analytic Riemannian metric on R N. We prove: 1. Each point of V has a neighborhood which is quasi-isometric (naturally and 'almost isometrically') to a union of metric cones and horns, glued at their tips. 2. A full asymptotic exp...
متن کاملLipschitz Geometry of Complex Surfaces: Analytic Invariants and Equisingularity
We prove that the outer Lipschitz geometry of the germ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities with constant Lipschitz geometry is Zariski equisingular. We also prove a strong converse for families of normal complex hypersurface singularities in C3: Zariski equ...
متن کامل