Shreeram S. Abhyankar

Resolution of Singularities of Embedded Algebraic Surfaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

Besides the description of the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic, this new edition provides a self-contained introduction to birational algebraic geometry, based only on commutative algebra. It also gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 312
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783662035801
• Artikelnr.: 53147367

Autorenporträt

Besides the description of the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic, this new edition provides a self-contained introduction to birational algebraic geometry, based only on commutative algebra. It also gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996.

Inhaltsangabe

0 Introduction.- 1. Local Theory.- 1 Terminology and preliminaries.- 2 Resolvers and principalizers.- 3 Dominant character of a normal sequence.- 4 Unramified local extensions.- 5 Main results.- 2. Global Theory.- 6 Terminology and preliminaries.- 7 Global resolvers.- 8 Global principalizers.- 9 Main results.- 3. Some Cases of Three-Dimensional Birational Resolution.- 10 Uniformization of points of small multiplicity.- 11 Three-dimensional birational resolution over a ground field of characteristic zero.- 12 Existence of projective models having only points of small multiplicity.- 13 Three-dimensional birational resolution over an algebraically closed ground field of charateristic ? 2, 3, 5.- Appendix on Analytic Desingularization in Characteristic Zero.- Additional Bibliography.- Index of Notation.- Index of Definitions.- List of Corrections.