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for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.

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Ramification divisor with base change

Let's work over $\mathbb{C}$. Consider the following commutative diagram \begin{array}{llllllllllll} E_1& \xrightarrow{f} &E_2\\ \downarrow{\pi} &&\downarrow{\pi}\\ P_1 & \xrightarrow{g} &P_2 \end{ar …
Sheng Meng's user avatar
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Ramification divisor with base change

So the answer is: Question 1 is wrong in general as R. van Dobben de Bruyn pointed out in the comment that the base change may not be normal. So there is no conflict in Main Question 3. See also the …
Sheng Meng's user avatar