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I am studying Riemann-Roch theorem but I have some difficulty understanding the concept of divisor of a differential form and the link between differential forms, their divisors and the RRT. Could you suggest some books to understand this topics! Thank you in advance!

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  • Rick Miranda's Algebraic curves and Riemann surfaces. If you already know the basics about Riemann surfaces and differential forms, you could start from chapter V. – lEm May 15 '19 at 14:30
  • Another beautiful classic reference is Griffiths's Introduction to Algebraic Curves. – Ted Shifrin May 15 '19 at 17:03
  • You can look in there a meromorphic function $f$ with $n$ poles is a $n$-fold holomorphic map to the Riemann sphere, by topological arguments we know how many branch points it must have, from which we know the number of zeros/poles of $df$ as well as $g df$ for any meromorphic function $g$ – reuns May 16 '19 at 18:25

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Check out the following sections from Otto Forster's Lectures on Riemann Surfaces:

$\S$9: Differential Forms

$\S$16: The Riemann-Roch Theorem

The latter section gives a gentle exposition of the link between differential forms and their divisors before discussing RRT. An upside of this book compared to Miranda's is the use of sheaf theoretic language, which I think is best introduced in a concrete context like the theory of Riemann surfaces.

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