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Please give a clear step proof for the following I. Let F : X - Y be a nonconstant holomorphic map between compact Rie- mann

image text in transcribedPlease give a clear step proof for the following

I. Let F : X - Y be a nonconstant holomorphic map between compact Rie- mann surfaces. 1. Show that if Y = P1, and F has degree at least two, then F must be ramified. 2. Show that if X and Y both have genus one, then F is unramified. 3. Show that g(Y) = g(X) always. 4. Show that if g(Y) = g(x) > 2, then F is an isomorphism. I. Let F : X - Y be a nonconstant holomorphic map between compact Rie- mann surfaces. 1. Show that if Y = P1, and F has degree at least two, then F must be ramified. 2. Show that if X and Y both have genus one, then F is unramified. 3. Show that g(Y) = g(X) always. 4. Show that if g(Y) = g(x) > 2, then F is an isomorphism

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