Authors:
- Provides a complete proof of desingularization of surfaces, and several other well-known results not previously published in the literature
- Briefly summarizes the history of the topic, with numerous readable references
- Written in an accessible style, ideal for non-specialists
- Features numerous useful computations, serving as a source of inspiration for experts exploring bigger dimensions
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2270)
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Table of contents (18 chapters)
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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Université Paris-Saclay, UVSQ, LMV (UMR 8100) CNRS, Versailles Cedex, France
Vincent Cossart
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Fakultät für Mathematik, Universität Regensburg, Regensburg, Germany
Uwe Jannsen
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Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Japan
Shuji Saito
Bibliographic Information
Book Title: Desingularization: Invariants and Strategy
Book Subtitle: Application to Dimension 2
Authors: Vincent Cossart, Uwe Jannsen, Shuji Saito
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-52640-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-52639-9Published: 28 August 2020
eBook ISBN: 978-3-030-52640-5Published: 27 August 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 258
Number of Illustrations: 41 b/w illustrations
Topics: Algebra, Algebraic Geometry