Topology of Algebraic Curves
An Approach via Dessins d'Enfants
Series:De Gruyter Studies in Mathematics 44
Aims and Scope
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.
- xvi, 393 pages
- Type of Publication:
- Trigonal Curve; Plane Sextic; Elliptic Surface; Lefschetz Fibration; Real Variety; Modular Group; Dessin d’Enfant; Braid Monodromy; Monodromy Factorization; Fundamental Group