• Corpus ID: 119734389

Lectures notes on compact Riemann surfaces

  title={Lectures notes on compact Riemann surfaces},
  author={Bertrand Eynard},
  journal={arXiv: Mathematical Physics},
  • B. Eynard
  • Published 16 May 2018
  • Mathematics
  • arXiv: Mathematical Physics
This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations. 2) Space of meromorphic functions and forms, we classify them with the Newton polygon. 3) Abel map, the Jacobian and Theta functions. 4) The Riemann--Roch theorem that computes the dimension of spaces of functions and forms with given orders of poles and… 

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