Desingularization: Invariants and Strategy

Application to Dimension 2

Häftad, Engelska, 2020

AvVincent Cossart,Uwe Jannsen,Shuji Saito

1 099 kr

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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;

Produktinformation

Utgivningsdatum2020-08-28
Mått155 x 235 x 15 mm
Vikt411 g
FormatHäftad
SpråkEngelska
SerieLecture Notes in Mathematics
Antal sidor258
FörlagSpringer Nature Switzerland AG
ISBN9783030526399

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Algebra inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

- 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.