# Representations of braid groups and construction of projective surfaces

## TL;DR

This paper explores how the algebraic-geometric representation theory of higher genus braid groups can be employed to construct novel examples of complex projective surfaces, linking braid groups to algebraic geometry.

## Contribution

It introduces a method to use higher genus braid group representations for constructing complex projective surfaces, expanding the applications of braid groups in algebraic geometry.

## Key findings

- New examples of complex projective surfaces constructed
- Connection established between braid group representations and algebraic geometry
- Potential applications in understanding surface invariants

## 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.