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Algebraic Curves and Riemann Surfaces


About this Title

Rick Miranda, Colorado State University, Fort Collins, CO

Publication: Graduate Studies in Mathematics
Publication Year 1995: Volume 5
ISBNs: 978-0-8218-0268-7 (print); 978-1-4704-1140-4 (online)
DOI: http://dx.doi.org/10.1090/gsm/005
MathSciNet review: MR1326604
MSC: Primary 14Hxx; Secondary 14-01, 30F99

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Table of Contents


Chapters

  • Chapter I. Riemann surfaces: Basic definitions
  • Chapter II. Functions and maps
  • Chapter III. More examples of Riemann surfaces
  • Chapter IV. Integration on Riemann surfaces
  • Chapter V. Divisors and meromorphic functions
  • Chapter VI. Algebraic curves and the Riemann-Roch theorem
  • Chapter VII. Applications of Riemann-Roch
  • Chapter VIII. Abel’s Theorem
  • Chapter IX. Sheaves and Čech cohomology
  • Chapter X. Algebraic sheaves
  • Chapter XI. Invertible sheaves, line bundles, and $\check {H}^1$