Topology of Algebraic Curves : : An Approach via Dessins d'Enfants / / Alex Degtyarev.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Degtyarev, Alex,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2012]; ©2012
• Year of Publication: 2012
• Language: English
• Series: De Gruyter Studies in Mathematics , 44
• Physical Description: 1 online resource (393 p.)

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.

Table of Contents

Frontmatter -- 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