Hurwitz schemes

The Hurwitz scheme $ \mathcal{H}_{d,g}$ parametrizes simply branched covers of $ \mathbf{P}^{1}$, i.e. pairs $ (C,\pi)$ of a genus $ g$ curve $ C$ and a degree $ d$ map $ \pi: C \rightarrow \mathbf{P}^{1}$ with simple ramification. Variations on this definition include allowing more complicated ramification behavior and higher genus targets.



Jeffrey Herschel Giansiracusa 2005-05-17