Desingularization: Invariants and Strategy
Application to Dimension 2
Published on 28. August 2020
Book
Paperback/Softback
VIII, 258 pages
978-3-030-52639-9 (ISBN)
Description
This book provides a rigorous and self-contained review of desingularization theory. Focusing on arbitrary dimensional schemes, it discusses the important concepts in full generality, complete with proofs, and includes an introduction to the basis of Hironaka's Theory.
The core of the book is a complete proof of desingularization of surfaces; despite being well-known, this result was no more than folklore for many years, with no existing references.
Throughout the book there are numerous computations on standard bases, blowing ups and characteristic polyhedra, which will be a source of inspiration for experts exploring bigger dimensions. Beginners will also benefit from a section which presents some easily overlooked pathologies.
More details
Product info
Book
Series
Edition
1st ed. 2020
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
41 s/w Abbildungen
VIII, 258 p. 41 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 15 mm
Weight
411 gr
ISBN-13
978-3-030-52639-9 (9783030526399)
DOI
10.1007/978-3-030-52640-5
Schweitzer Classification
Other editions
Additional editions
Vincent Cossart | Uwe Jannsen | Shuji Saito
Desingularization: Invariants and Strategy
Application to Dimension 2
E-Book
08/2020
Springer
€85.59
Available for download
Persons
Content
- Introduction. - Basic Invariants for Singularities. - Permissible Blow-Ups. B-Permissible Blow-Ups: The Embedded Case. - B-Permissible Blow-Ups: The Non-embedded Case. - Main Theorems and Strategy for Their Proofs. - (u)-standard Bases. - Characteristic Polyhedra of J ? R. - Transformation of Standard Bases Under Blow-Ups. - Termination of the Fundamental Sequences of B-Permissible Blow-Ups, and the Case ex(X) = 1. - Additional Invariants in the Case ex(X) = 2. - Proof in the Case ex(X) = esx(X) = 2, I: Some Key Lemmas. - Proof in the Case ex(X) = ex(X) = 2, II: Separable Residue Extensions. - Proof in the Case ex(X) = ex(X) = 2, III: Inseparable Residue Extensions. - Non-existence of Maximal Contact in Dimension 2. - An Alternative Proof of Theorem 6.17. - Functoriality, Locally Noetherian Schemes, Algebraic Spaces and Stacks. - Appendix by B. Schober: Hironaka's Characteristic Polyhedron. Notes for Novices.