I feel that this may be related to the Riemann Roch theorem or Riemann Hurwiz formula but I'm not sure how. If you could provide a good reference and what to look for I would be very grateful.
Is there an integral formula for the degree of a holomorphic embedding of the Riemann sphere into projective space?
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algebraic-geometry
riemann-surfaces
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0What is the data that you want your formula to be in terms of? – 2017-01-12
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0You have a map $\mathbb{C}\mathbb{P}^1\rightarrow \mathbb{C}\mathbb{P}^n$, I was thinking there might be a formula using the differential of this map or something of that nature. – 2017-01-12
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0What I was getting at is that there are many different such maps, with different degrees. Indeed, Mohan explained the situation for $n=3$ in comments to one of your previous questions. – 2017-01-12
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0Thanks, yes that was useful to me. I'm talking about if you have a specific map, and you want to find the degree using an integral formula. I think I more or less understand Mohan's previous answer at this point. – 2017-01-12
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0I'm reading Griffiths and Harris and I think I might be looking for something related to the Wirtinger theorem (pg. 171 of G and H). I'm going to think about it some more but this is looking helpful. – 2017-01-15