Topology of Algebraic Curves

An Approach via Dessins d'Enfants

Alex Degtyarev

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English

De Gruyter
14 June 2012

Algebra; Geometry; Algebraic topology

Series: De Gruyter Studies in Mathematics

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.

By: Alex Degtyarev
Imprint: De Gruyter
Country of Publication: Germany
Volume: 44
Dimensions: Height: 240mm, Width: 170mm, Spine: 24mm
Weight: 827g
ISBN: 9783110255911
ISBN 10: 311025591X
Series: De Gruyter Studies in Mathematics
Pages: 409
Publication Date: 14 June 2012
Recommended Age: College Graduate Student
Audience: Professional and scholarly , Undergraduate , Undergraduate
Format: Hardback
Publisher's Status: Active

Alex Degtyarev, Bilkent University, Ankara, Turkey.

Reviews for Topology of Algebraic Curves: An Approach via Dessins d'Enfants

[...] The book is principally designated to researches and graduate students in topology of (complex and real) algebraic varieties, but the monograph is also very useful for mathematicians working in other fields. Ilia Itenberg, Zentralblatt fr Mathematik