Desingularization: Invariants and Strategy

Application to Dimension 2

AvVincent Cossart,Uwe Jannsen

Häftad, Engelska, 2020

Del 2270 i serien Lecture Notes in Mathematics

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Beskrivning

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

Utgivningsdatum:2020-08-28
Mått:155 x 235 x 15 mm
Vikt:411 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:258
Förlag:Springer Nature Switzerland AG
ISBN:9783030526399

Utforska kategorier

Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Innehållsförteckning

- 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.