Finite quotients of surface braid groups and double Kodaira fibrations

Abstract

Let ${\Sigma }_b$ be a closed Riemann surface of genus $b$. We give an account of some results obtained in the recent papers \cite{CaPol19, Pol20, PolSab21} and concerning what we call here \emph{pure braid quotients},namely non-abelian finite groups appearing as quotients of the pure braid group on two strands ${\mathsf{P}}_2({\Sigma }_b)$. We also explain how these groups can be used in order to provide new constructions of double Kodaira fibrations.

23 pages, 3 figures. To appear in "The Art of Doing Algebraic Geometry", a Springer volume dedicated to Ciro Ciliberto. arXiv admin note: text overlap with arXiv:2102.04963, arXiv:2002.01363, arXiv:1905.03170

References in corpus (3)

• Surface braid groups, finite Heisenberg covers and double Kodaira fibrations
• Diagonal double Kodaira structures on finite groups
• Extra-special quotients of surface braid groups and double Kodaira fibrations with small signature