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

Format:

Book

Author/Creator:

Degtyarev, A. (Alexander), 1962-

Series:

De Gruyter Studies in Mathematics

De Gruyter studies in mathematics, 0179-0986 ; 44

Language:

English

Subjects (All):

Curves, Plane.

Topological degree.

Physical Description:

1 online resource (412 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, c2012.

Language Note:

English

Summary:

This monograph summarizes and extends a number of results on the topology of trigonal curves in geometrically ruled surfaces. An emphasis is given to various applications of the theory to a few related areas, most notably singular plane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex and real), and Hurwitz equivalence of braid monodromy factorizations. The approach relies on a close relation between trigonal curves/elliptic surfaces, a certain class of ribbon graphs, and subgroups of the modular group, which provides a combinatorial framework for the study of geometric objects. A brief summary of the necessary auxiliary results and techniques used and a background of the principal problems dealt with are included in the text. The book is intended to researchers and graduate students in the field of topology of complex and real algebraic varieties.

Contents:

Front matter

Preface

Contents

Part I. Skeletons and dessins

Chapter 1. Graphs

Chapter 2. The groups Γ 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 Σd

Appendix C. Computer implementations

Appendix D. Definitions and notation

Bibliography

Index of figures

Index of tables

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [369]-378) and indexes.

ISBN:

9786613940186

9781283627733

1283627736

9783112204122

3112204123

OCLC:

811962933