Kurzbeschreibung:
This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic trick employed in the original edition of the book. This new edition will inspire further progress in resolution of singularities of algebraic and arithmetical varieties which will be valuable for applications to algebraic geometry and number theory. The book can be used for a second year graduate course. The reference list has been updated.
Inhaltsverzeichnis:
From the contents: Local Theory.-Resolvers and principalizers,Dominant character of a normal sequence,Unramified local extensions, Global Theory.-Global resolvers, Global prinzipalizers,Some Cases of Three-Dimensional Birational Resolution.-Uniformization of points of small multiplicity, Three-dimensional birational resolution over a ground field of characteristic zero and over an algebraically closed ground field of characteristic = 2, 3, 5, Existence of projective models having only points of small multiplicity, Analytic desingularization in characteristic zero
