Hurwitz equivalence of braid monodromies and extremal elliptic surfaces
Date
2011
Authors
Degtyarev, A.
Advisor
Instructor
Source Title
Proceedings of the London Mathematical Society
Print ISSN
0024-6115
Electronic ISSN
1460-244X
Publisher
Wiley
Volume
103
Issue
6
Pages
1083 - 1120
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract
We discuss the equivalence between the categories of certain ribbon graphs and subgroups of the modular group Γ and use this equivalence to construct exponentially large families of not Hurwitz equivalent simple braid monodromy factorizations of the same element. As an application, we also obtain exponentially large families of topologically distinct algebraic objects such as extremal elliptic surfaces, real trigonal curves, and real elliptic surfaces. © 2011 London Mathematical Society.