# MA475 Riemann Surfaces

Example Sheets for 2020:

Lecture notes from 2020:

Older material is listed below.

Lecture notes for 2019:

Lecture 9 The sphere, Group actions

Lecture 10 The torus. Main theorem statement

Lecture 12 Hyper-elliptic surfaces

Lecture 13 More hyper-elliptic discussion

Lecture 14 Meromorphic functions, isolated singularities

Lecture 15 Meromorphic functions on S^2

Lecture 16 Local form for holomorphic functions

Lecture 17 Holomorphic 1 forms

Lecture 18 Holomorphic 1 forms on C^2

Lecture 24 Weierstrass function

Lecture 25 Polynomial equation

Lecture 26 Conformal isomorphism

Lecture 27 Integration and periods

Lecture 29 Functions on moduli space

Lecture 30 Geometry of 1-forms

Example sheets for 2019:

Course contents for 2018:

Definition of Riemann surfaces (Uploaded 13 April)

Implicit function theorem (Uploaded 16 April)

Affine and projective varieties (Uploaded May 14)

Local structure of holomorphic maps and structure of proper holomorphic maps (Uploaded 16 April)

Meromorphic functions on CP1 (Uploaded 15 April)

2018 Covering space notes (Updated 11 April)

2018 Weierstrass P functions and Riemann-Hurwitz (Updated 15 April)

Lecture notes from 2017:

Riemann surfaces and atlases

Algebraic curves and holomorphic maps

Topology and holomorphic maps

The Weierstrass P function

The uniformisation theorem and conclusion