Hurwitz scheme

In algebraic geometry, the Hurwitz scheme ${\displaystyle {\mathcal {H}}_{d,g}}$ is the scheme parametrizing pairs (${\displaystyle C,\pi :C\to \mathbf {P} ^{1}}$) where C is a smooth curve of genus g and π has degree d.^[1]

References

1. Joe Harris and Ian Morrison. Moduli of curves.