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Desingularization: Invariants and Strategy

Desingularization: Invariants and Strategy

Wydawnictwo Springer Nature Customer Service Center GmbH
Data wydania 01/08/2020
Wydanie Pierwsze
Liczba stron 258
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9783030526399
Kategorie Algebra, Geometria algebraiczna
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Opis książki

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.

Desingularization: Invariants and Strategy

Spis treści

- 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.

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