Alex Degtyarev

Topology of Algebraic Curves
An Approach via Dessins d'Enfants

To Ayse

This page is a shameless advertisement of my new monograph: Some parts of the book are based on my joint works with Ilia Itenberg, Viatcheslav Kharlamov, and Nermin Salepci
Abstract: The book is an attempt to summarize and extend 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 researches and graduate students in the field of topology of complex and real algebraic varieties.

Mathematical Subject Classification:   Primary: 14H30, 14H50, 14J27, 14P25; Secondary: 20F36, 11F06, 05C90, 14H57
Keywords and Phrases:   trigonal curve, plane sextic, elliptic surface, Lefschetz fibration, real variety, modular group, dessin d'enfant, braid monodromy, monodromy factorization, fundamental group
Level and Target Group:   Researchers and graduate students; monograph
Fields of Interest of a Potential Reader:   Main: topology of algebraic varieties; Related: algebraic geometry, singularity theory, real algebraic geometry
  • Preface and Table of Contents
  • GAP files for download (some proofs found in the book are heavily computer aided)

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