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Singular Algebraic Curves: With an Appendix by Oleg Viro by Gert-Martin Greuel

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Last updated on 05 Dec, 2024 13:04:54 GMTView all revisionsView all revisions

Item specifics

Condition
New: A new, unread, unused book in perfect condition with no missing or damaged pages. See the ...
Book Title
Singular Algebraic Curves: With an Appendix by Oleg Viro
Publication Date
2019-01-10
Pages
553
ISBN
9783030033491

About this product

Product Identifiers

Publisher
Springer International Publishing A&G
ISBN-10
303003349X
ISBN-13
9783030033491
eBay Product ID (ePID)
19038602362

Product Key Features

Number of Pages
Xx, 553 Pages
Language
English
Publication Name
Singular Algebraic Curves
Subject
Geometry / Algebraic
Publication Year
2019
Type
Textbook
Subject Area
Mathematics
Author
Eugenii Shustin, Gert-Martin Greuel, Christoph Lossen
Series
Springer Monographs in Mathematics Ser.
Format
Hardcover

Dimensions

Item Weight
36 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Reviews
"The book is very well written and sufficiently self-contained. Certainly, the reader is assumed to be familiar with the basics of algebraic geometry and singularity theory; however, most necessary results, even classical, are carefully stated and either proved in the book or supplied with abundant references. As a nice surprise, the book has an appendix on patchworking, which is the first English publication of the original text by Oleg Viro." (Alex Degtyarev, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 123, 2021) "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), "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)
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
Zero-Dimensional Schemes for Singularities.- Global Deformation Theory.- H 1-Vanishing Theorems.- Equisingular Families of Curves.
Synopsis
Zero-Dimensional Schemes for Singularities.- Global Deformation Theory.- H 1-Vanishing Theorems.- Equisingular Families of Curves., 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.
LC Classification Number
QA564-609

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