Riemann Surfaces

Math 213b / 10:30-11:45 Tu Th / Science Center room 507
Harvard University - Spring 2019

Instructor: Curtis T McMullen (ctm@math.harvard.edu)

Required Texts
  • Forster, Lectures on Riemann Surfaces, Springer-Verlag, 1981
Additional references
  • Buser, Geometry and Spectra of Compact Riemann Surfaces, Birkhauser, 1992
  • Griffiths and Harris, Principles of Algebraic Geometry, Wiley Interscience, 1978
  • Farkas and Kra, Riemann Surfaces, Springer-Verlag
Prerequisites. Intended for graduate students. Prerequesites include algebraic topology, complex analysis and differential geometry on manifolds.

Topics. This course will cover fundamentals of the theory of compact Riemann surfaces from an analytic and topological perspective. Topics may include:
  • Algebraic functions and branched coverings of P1
  • Sheaves and analytic continuation
  • Curves in projective space; resultants
  • Holomorphic differentials
  • Sheaf cohomology
  • Line bundles and projective embeddings; canonical curves
  • Riemann-Roch and Serre duality via distributions
  • Jacobian variety
Reading and Lectures. Students are responsible for all topics covered in the readings and lectures. Lectures may go beyond the reading, and not every topic in the reading will be covered in class.

Grades. Grades will be entirely based on homework. Graduate students who have passed their quals are encouraged to hand in at least 1 homework each month.

Homework. Homework will be assigned every week. Collaboration between students is encouraged, but you must write your own solutions, understand them and give credit to your collaborators. Late homework is not accepted, but your lowest homework score will be dropped.

Course home page: http://math.harvard.edu/~ctm/math213b