Topology of algebraic curves : an approach via dessins d'enfants

Topology of algebraic curves : an approach via dessins d'enfants / Alex Degtyarev.

The book summarizes the state and new results on the topology of trigonal curves in geometrically ruled surfaces. Emphasis is placed upon various applications of the theory to related areas, most notably singularplane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex...

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Bibliographic Details
Main Author: Degtyarev, A. (Alexander), 1962- (Author)
Format: eBook
Language:English
Published: Berlin ; Boston : De Gruyter, [2012]
Series:De Gruyter studies in mathematics ; 44.
Subjects:
Curves, Plane.
Topological degree.
MATHEMATICS > Geometry > Algebraic.
Curves, Plane
Topological degree
Algebraische Kurve
Topologische Graphentheorie
Online Access:Click for online access
Table of Contents:
  • Frontmatter
  • Preface
  • Contents
  • Part I. Skeletons and dessins
  • Chapter 1. Graphs
  • Chapter 2. The groups [Gamma] and B3
  • Chapter 3. Trigonal curves and elliptic surfaces
  • Chapter 4. Dessins
  • Chapter 5. The braid monodromy
  • Part II. Applications
  • Chapter 6. The metabelian invariants
  • Chapter 7. A few simple computations
  • Chapter 8. Fundamental groups of plane sextics
  • Chapter 9. The transcendental lattice
  • Chapter 10. Monodromy factorizations
  • Appendices
  • Appendix A. An algebraic complement
  • Appendix B. Bigonal curves in [Sigma]d
  • Appendix C. Computer implementations
  • Appendix D. Definitions and notation
  • Bibliography
  • Index of figures
  • Index of tables
  • Index.

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