Abstract
A differential will be said to be of the first kind if it is holomorphic everywhere on the Riemann surface. Such differentials form a vector space over the complex, and by the Riemann-Roch theorem, one sees that the dimension of this space is equal to the genus g of R.
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© 1972 Springer-Verlag New York Inc.
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Lang, S. (1972). The Theorem of Abel-Jacobi. In: Introduction to Algebraic and Abelian Functions. Graduate Texts in Mathematics, vol 89. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5740-0_4
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DOI: https://doi.org/10.1007/978-1-4612-5740-0_4
Publisher Name: Springer, New York, NY
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