
Singular Algebraic Curves
With an Appendix by Oleg Viro
Springer (Publisher)
Published on 10. January 2019
Book
Hardback
XX, 553 pages
978-3-030-03349-1 (ISBN)
Description
Singular algebraic curves have been in the focus of study in algebraic geometry from the very beginning, and till now remain a subject of an active research related to many modern developments in algebraic geometry, symplectic geometry, and tropical geometry. The monograph suggests a unified approach to the geometry of singular algebraic curves on algebraic surfaces and their families, which applies to arbitrary singularities, allows one to treat all main questions concerning the geometry of equisingular families of curves, and, finally, leads to results which can be viewed as the best possible in a reasonable sense. Various methods of the cohomology vanishing theory as well as the patchworking construction with its modifications will be of a special interest for experts in algebraic geometry and singularity theory. The introductory chapters on zero-dimensional schemes and global deformation theory can well serve as a material for special courses and seminars for graduate and post-graduate students.Geometry in general plays a leading role in modern mathematics, and algebraic geometry is the most advanced area of research in geometry. In turn, algebraic curves for more than one century have been the central subject of algebraic geometry both in fundamental theoretic questions and in applications to other fields of mathematics and mathematical physics. Particularly, the local and global study of singular algebraic curves involves a variety of methods and deep ideas from geometry, analysis, algebra, combinatorics and suggests a number of hard classical and newly appeared problems which inspire further development in this research area.
Reviews / Votes
"The book is written in a very clear style, many topics are illustrated by various nice pictures, visual diagrams, etc. ... this book is comprehensible, interesting and useful for graduate and post-graduate students; it is also very valuable for advanced researchers, lecturers, and practicians working in singularity theory, algebraic geometry, topology, combinatorics, tropical geometry and in other fields of mathematics and its applications." (Aleksandr G. Aleksandrov, zbMATH 1411.14001, 2019)More details
Product info
Book
Series
Edition
1st ed. 2018
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
74 s/w Abbildungen
Bibliographie
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 37 mm
Weight
1021 gr
ISBN-13
978-3-030-03349-1 (9783030033491)
DOI
10.1007/978-3-030-03350-7
Schweitzer Classification
Other editions
Additional editions

Gert-Martin Greuel | Christoph Lossen | Eugenii Shustin
Singular Algebraic Curves
With an Appendix by Oleg Viro
E-Book
12/2018
1st Edition
Springer
€139.09
Available for download
Content
Zero-Dimensional Schemes for Singularities.- Global Deformation Theory.- H 1-Vanishing Theorems.- Equisingular Families of Curves.