Representations of braid groups and construction of projective surfaces

Abstract

Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will focus on their algebraic-geometric aspects, explaining how the representation theory of higher genus braid groups can be used to produce interesting examples of projective surfaces defined over the field of complex numbers.

Note written for the Proceedings of the Conference "Group 32 - The 32nd International Colloquium on Group Theoretical Methods in Physics", held on Czech Technical University (Prague) on July 9-13, 2018

References in corpus (2)

• A family of surfaces with $p_g=q=2,K^2=7$ and Albanese map of degree $3$
• Monodromy representations and surfaces with maximal Albanese dimension