Math 625, Riemann Surfaces

Fall 2018

Instructor: Richard Hain

Text: R. Miranda: Algebraic Curves and Riemann Surfaces, Graduate Studies in Mathematics, Vol 5, American Mathematical Society, 1995.


  1. C. H. Clemens: Herbert A scrapbook of complex curve theory (Second edition), Graduate Studies in Mathematics, 55, American Mathematical Society, Providence, RI, 2003.
  2. M. Cornalba: The theorems of Riemann-Roch and Abel, Lectures on Riemann surfaces (Trieste, 1987), 302-349, World Sci. Publ., 1989. (pdf)
  3. Donaldson, Simon: Riemann Surfaces, Oxford University Press, 2011.
  4. H. Farkas, I. Kra: Riemann Surfaces, Graduate Texts in Mathematics, 71. Springer-Verlag, New York, 1980.
  5. Forster, Otto: Lectures on Riemann surfaces, Graduate Texts in Mathematics, 81. Springer-Verlag, New York, 1991.
  6. Phillip Griffiths: Introduction to algebraic curves, Translations of Mathematical Monographs, 76. American Mathematical Society, Providence, RI, 1989.
  7. Phillip Griffiths, Joseph Harris: Principles of algebraic geometry, Wiley Classics. (ff. Chapter 2).
  8. R. C. Gunning: Lectures on Riemann surfaces, Princeton Mathematical Notes Princeton University Press, Princeton, N.J. 1966.
  9. David Mumford: Curves and their Jacobians, The University of Michigan Press, Ann Arbor, Mich., 1975.
The most basic of these are the books by Forster, Farkas and Kra, Griffiths (his China lectures) and Gunning. Mumford's lectures have been reprinted as part of his Red Book of Varieties and Schemes.




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