Take the equation $y^{d}=\Pi_{1}^{n}(x-t_{i})^{m_{i}}$ over $\mathbb{C}$. This affine equation gives a cyclic cover of $\mathbb{P}^{1}$. Now it is usually said without explanation that if the sum $\sum m_{i}$ is not divisible by $d$, then the family is ramified over $\infty$. My question is how to see explicitly--in terms of equations maybe--that this is the case.
How to explicitly see the ramification over infinity
Darius Math
- 2.2k
- 15
- 24