Topology of Algebraic Curves: An Approach via Dessins d'Enfants: 44 (De Gruyter Studies in Mathematics, 44)

Product description Review "[...] 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 für Mathematik Review "[...] 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 für Mathematik From the Back Cover 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. About the Author Alex Degtyarev, Bilkent University, Ankara, Turkey. Read more