Download or read book Desingularization: Invariants and Strategy written by Vincent Cossart and published by Springer Nature. This book was released on 2020-08-27 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rigorous and self-contained review of desingularization theory. Focusing on arbitrary dimensional schemes, it discusses the important concepts in full generality, complete with proofs, and includes an introduction to the basis of Hironaka’s Theory. The core of the book is a complete proof of desingularization of surfaces; despite being well-known, this result was no more than folklore for many years, with no existing references. Throughout the book there are numerous computations on standard bases, blowing ups and characteristic polyhedra, which will be a source of inspiration for experts exploring bigger dimensions. Beginners will also benefit from a section which presents some easily overlooked pathologies.