Families of Curves Wanted

An interesting problem

Let \(n\) be a large positive integer.  Recently I've been looking for a family of curves \(f_n: \mathscr{C}_n\to \mathbb{P}^1\) with the following properties:

  • \(f_n\) is flat and proper of relative dimension \(1\),
  • the general fiber of \(f_n\) is smooth, and the family is not isotrivial
  • every singularity that appears in a fiber of \(f_n\) is etale-locally of the form $$xy=t^n$$ where \(t\) is a parameter on \(\mathbb{P}^1\)...
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