On the Resolution of Higher Singularities of Algebraic Curves Into Ordinary
Language: English
Published by Forgotten Books, 2022
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.70
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book explores the resolution of higher singularities of algebraic curves into ordinary nodes for the first time. The author, an eminent mathematician, provides new proof of a fundamental theorem established by Max Noether in 1875. The author carries out an idea originally proposed by Felix Klein to transform the plane curve into a curve in space having no singular points. Then, the resulting space curve is projected into a plane curve with no other singularities than ordinary double points. Mathematical theory is enriched with a number of auxiliary theorems on triply infinite systems of cubics, enhancing our understanding of the properties and behavior of these systems. Overall, this book offers valuable insights into the resolution of singularities of algebraic curves, expanding our knowledge in this field of mathematics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781332337071_0
- Title
- On the Resolution of Higher Singularities of Algebraic Curves Into Ordinary
- Author
- B. M. Walker
- Publisher
- Forgotten Books
- Publication year
- 2022
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332337074
- ISBN 13
- 9781332337071
- Seller catalogs
- Geometry
Transforming singularities into ordinary nodes: a detailed, new approach to resolving algebraic curves
This lucid treatment presents a new proof that a plane algebraic curve with ordinary multiple points can be transformed into a space curve and projected back to a plane curve with only ordinary double points. The work builds from a geometric idea attributed to Klein, and methodically develops a concrete path to the resolution process.
The book lays out the transformation in four chapters, explaining how a given curve is moved from the plane to a cubic surface, and how successive projections reduce complex singularities to simple nodes. It discusses triply infinite linear systems of plane cubics, canonical forms, and how bases of cubics relate to the six fundamental points. Readers will see how ordinary points and multiple points behave under the transformation, and how tangents and cycles guide the process toward a curve with only ordinary nodes.- How to model cubics through six fixed points and its implications for the transformation
- How ordinary and multiple points on the original curve map to the transformed curve
- How to control tangents and cycles to avoid coinciding singularities
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Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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