Topology of Algebraic Curves
An Approach via Dessins d'Enfants
This page is a shameless
advertisement of my new monograph:
Some parts of the book are based on my joint works with
Viatcheslav Kharlamov, and
Alex Degtyarev, Topology of Algebraic Curves: An Approach via Dessins d'Enfants.
De Gruyter Studies in Mathematics, 44.
Walter de Gruyter & Co., Berlin, 2012. xvi+393 pp.
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:
Keywords and Phrases:
Level and Target Group:
Researchers and graduate students; monograph
Fields of Interest of a Potential Reader:
topology of algebraic varieties;
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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