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Singular Algebraic Curves

With an Appendix by Oleg Viro

  • Gert-Martin Greuel
  • Christoph Lossen
  • Eugenii Shustin

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
    Pages 1-110
  3. Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
    Pages 111-267
  4. Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
    Pages 269-332
  5. Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
    Pages 333-487
  6. Back Matter
    Pages 489-553

About this book

Introduction

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.

Keywords

14-02; 14Hxx; 14H10; 14H20; 14F17 14B07; 14M25; 14J60; 14P25;14Q05 Algebraic Curves Equisingular Families of Curves Zero-Dimensional Schemes Cohomology Vanishing Theory

Authors and affiliations

  • Gert-Martin Greuel
    • 1
  • Christoph Lossen
    • 2
  • Eugenii Shustin
    • 3
  1. 1.Fachbereich MathematikTU KaiserslauternKaiserslauternGermany
  2. 2.Fachbereich MathematikTU KaiserslauternKaiserslauternGermany
  3. 3.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-03350-7
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-03349-1
  • Online ISBN 978-3-030-03350-7
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site