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arXiv · 2103.07921

The relative Riemann-Hurwitz formula

Zhiguo Ding·Michael E. Zieve
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Abstract

For any nonconstant f,g in C(x) such that the numerator H(x,y) of f(x)-g(y) is irreducible, we compute the genus of the normalization of the curve H(x,y)=0. We also prove an analogous formula in arbitrary characteristic when f and g have no common wildly ramified branch points, and generalize to (possibly reducible) fiber products of nonconstant morphisms of curves f:A-->D and g:B-->D.

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Zhiguo Ding, Michael E. Zieve. 2021-03-14. The relative Riemann-Hurwitz formula. https://arxiv.org/abs/2103.07921

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