The relative Riemann-Hurwitz formula
Algebraic Geometry
2021-03-16 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.2103.07921,
title = {The relative Riemann-Hurwitz formula},
author = {Zhiguo Ding and Michael E. Zieve},
journal= {arXiv preprint arXiv:2103.07921},
year = {2021}
}
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11 pages