Desingularization : invariants and strategy : application to dimension 2 /: invariants and strategy : application to dimension 2. (2020)

• Record Type: Book
• Further Information: Note: Vincent Cossart, Uwe Jannsen, Shuji Saito.
• Other Names: Cossart, Vincent, 1950-; Jannsen, Uwe; Saitō, Shūji, 1957-
• Contents: Intro -- Abstract -- Contents -- 1 Introduction -- 1.1 What Is Desingularization? -- 1.2 Very Short History of Desingularization -- 1.3 How Did we Start? -- 1.4 Summary -- 1.5 Conventions and Concluding Remarks -- 2 Basic Invariants for Singularities -- 2.1 Invariants of Graded Rings and Homogeneous Ideals in Polynomial Rings -- 2.2 Invariants for Local Rings -- 2.3 Invariants for Schemes -- 3 Permissible Blow-Ups -- 4 B-Permissible Blow-Ups: The Embedded Case -- 5 B-Permissible Blow-Ups: The Non-embedded Case -- 6 Main Theorems and Strategy for Their Proofs -- 7 (u)-standard Bases 8 Characteristic Polyhedra of JR -- 9 Transformation of Standard Bases Under Blow-Ups -- 10 Termination of the Fundamental Sequences of B-Permissible Blow-Ups, and the Case e_x(X)=1 -- 11 Additional Invariants in the Case e_x(X)=2 -- 12 Proof in the Case e_x(X)=\overline{e}_x(X)=2, I: Some Key Lemmas -- 13 Proof in the Case e_x(X)=\overline{e}_x(X)=2, II: Separable Residue Extensions -- 14 Proof in the Case e_x(X)=\overline{e}_x(X)=2, III: Inseparable Residue Extensions -- 15 Non-existence of Maximal Contact in Dimension 2 -- 16 An Alternative Proof of Theorem 6.17 17 Functoriality, Locally Noetherian Schemes, Algebraic Spaces and Stacks -- 18 Appendix by B. Schober: Hironaka's Characteristic Polyhedron. Notes for Novices -- 18.1 Introduction -- 18.2 The Newton Polyhedron of an Ideal -- 18.3 The Projected Polyhedron and Its Relation to the Newton Polyhedron -- 18.4 The Directrix and Its Role: Choosing (u) -- 18.5 Determining the Characteristic Polyhedron: Optimizing the Choice of (f -- y) -- 18.6 Invariants from the Polyhedron and the Effect of Blowing Up -- References -- Index
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 514/.746; Singularities (Mathematics); Invariants; Dimension theory (Algebra); Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030526405; 3030526402
• Related ISBNs: 3030526399; 9783030526399
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.