Resolution of Singularities

textbook for part of a one-year introductory sequence in algebraic geometry for students who have some familiarity with algebraic geometry and commutative algebra at the level of introductory courses in them. Annotation 2004 Book News, Inc., Portland, OR (booknews.com).

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 cha

Introduction; Non-singularity and resolution of singularities; Curve singularities; Resolution type theorems; Surface singularities; Resolution of singularities in characteristic zero; Resolution of surfaces in positive characteristic; Local uniformization and resolution of surfaces; Ramification of valuations and simultaneous resolution; Smoothness and non-singularity; Bibliography; Index