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Darius Math
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How to explicitely see the ramification over infinity

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.

Darius Math
  • 2.2k
  • 15
  • 24