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I'm not an expert in the field but I have few comments to make: 1. Why the article, needs to be titled "Differentials of the first kind", while there is no independent article for the second and the third kind. I think we should change the title to "Abelian
Differentials" and put two (or three)
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If you search google books for differentials and "third kind" or "second kind" you find books by
Chvalley and Griffiths: they say a meromorphic one-form on a Riemann surface is of the
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3. I don't see that integral as the high light of using differentials, while there are essential to cohomology theory for example. I think we have more important stuff to put here.
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4. Finally, I agree with above comment, we need to make the definition of the second and third kind obvious in the article instead of a giving a general unrelated description.
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hi , i find it totally inappropriate the math symbols you use please use latex thank you 03:06, 4 April 2007 86.107.226.222
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sections for each kind. The fact that "Abelian
Differential" is redirected to this page is even more reason to do so.
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2. The elliptic integral is a special case of hyper elliptic integral and shouldn't be excluded, i.e., degree : -->
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I have to give a talk on the differentials of the second kind, after which I'll come back and update the article.
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Yes. What this article currently says does not quite align with standard textbooks.
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Yes. I am reviewing Jost now, and this is the terminology he uses, too.
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Someone should correct/adjust this article it seems.
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2) second kind, if it has zero residues at each pole
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