Resolution of singularities
By: Steven Dale Cutkosky
Series: Graduate studies in mathematics -- v. 63
Publisher: American Mathematical Society
Published: 2004
Place of publication: Providence, R.I
Language: eng
Number of pages: 186
ISBN-13: 9780821835555
Subjects: Singularities (Mathematics)
Description: "The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic." "The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of D-modules, topology, and mathematical physics." "This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic." "Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing insight and intuition for the novice (or expert). There are many examples and exercises throughout the text." "The book is suitable for a second course on a topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves."--BOOK JACKET.
Notes: Includes bibliographical references (p. 179-183) and index