Hurwitz scheme

In algebraic geometry, the Hurwitz scheme $\backslash mathcal\{H\}\_\{d,\; g\}$ is the scheme parametrizing pairs ($C,\; \backslash pi:\; C\; \backslash to\; \backslash mathbf\{P\}^1$) where C is a smooth curve of genus g and {{pi}} has degree d.Joe Harris and Ian Morrison. Moduli of curves.