Resolution of Singularities of Embedded Algebraic Surfaces

Download or read book Resolution of Singularities of Embedded Algebraic Surfaces written by Shreeram Shankar Abhyankar and published by . This book was released on 1966 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.