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Description: The course will focus on presenting an up to date survey of the many facets of the
modern theory of algebraic curves (Riemann surfaces) and their moduli spaces, with an emphasis on concrete and computational issues. Topics to be covered include the geometry of the moduli space of curves,
an introduction to the Hurwitz theory of counting covers of algebraic curves, Brill-Noether theory (both the
classical and the tropical approach) and the connection between curves and graph theory.
As general references, apart from well-established papers, we shall use:
1) Harris, Morrison: Moduli of curves, Springer
2) Cavalieri: Riemann surfaces and algebraic curves: A first course in Hurwitz theory
3) Arbarello, Cornalba, Griffiths, Harris: Geometry of algebraic curves. |
