Alex Degtyarev
Gebundenes Buch

Topology of Algebraic Curves

An Approach via Dessins d'Enfants

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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 g...