A remark to analytic geometry

An Introduction to Rigid Analytic Geometry

These notes are intended to be a short course in rigid analytic geometry, without, however, providing always proofs. The excellent book [4] by Bosch, Güntzer and Remmert is an extensive introduction into rigid analytic geometry, and includes all the proofs I have omitted here.

A Remark on ’some Numerical Results in Complex Differential Geometry’

In order to find explicit numerical approximation of Kähler-Einstein metric of projective manifolds, Donaldson introduced in [3] various operators with good properties to approximate classical operators. See the discussions in Section 4.2 of [3] for more details related to our discussion. In this note we verify certain statement of Donaldson about the operator QK in Section 4.2 by using the ful...

Overview of Rigid Analytic Geometry

The idea is simple: we want to develop a theory of analytic manifolds and spaces over fields equipped with an arbitrary complete valuation. Of course, it is a standard fact that such a field must be either R, C, or a field with a nonarchimedean valuation, so what we really mean is that we want to develop a theory of nonarchimedean analytic spaces. Doing this näıvely (i.e., defining manifolds in...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Two Lemmas in Local Analytic Geometry

We prove two results about the local properties of generically one to one analytic mappings. Version: .76; Revised: 12–15–98; Run: March 23, 1999 §1: Introduction In this paper we consider two local properties of analytic maps which are generically one to one. First we consider holomorphic maps from open sets in C which behave locally like monoidal transformations: Let (z, w) denote coordinates...