Topology of Algebraic Curves An Approach via Dessins d'Enfants

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 fibrat...

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Bibliographic Details
Main Author: Degtyarev, Alex
Format: eBook
Language:English
Published: Berlin De Gruyter [2012]©2012, 2012
Series:De Gruyter Studies in Mathematics
Subjects:
Online Access:
Collection: DeGruyter MPG Collection - Collection details see MPG.ReNa
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653 |a Curves, Plane 
653 |a Topological degree 
653 |a Algebra 
653 |a Real Variety 
653 |a Dessin d'Enfant 
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520 |a 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