Answer by Matthew Morrow for How does $f_* O_X$ measure ramification and...
The following does not exactly answer your question, but you may find it interesting. It is the Riemann-Hurwitz formula for surfaces.Let $\phi:S_1\to S_2$ be a finite morphism between smooth,...
View ArticleHow does $f_* O_X$ measure ramification and Grothendieck-Riemann-Roch
Let $f:X\longrightarrow Y$ be a finite morphism of smooth projective varieties over a field $k$ of characteristic zero, where $\dim X=\dim Y$. Then $f$ is flat. Hence $f_\ast \mathcal{O}_X$ is a...
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