Enrollment year
2020/2021
Academic discipline
MAT/03 (GEOMETRY)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Curriculum
PERCORSO COMUNE
Period
2nd semester (01/03/2021 - 11/06/2021)
Lesson hours
48 lesson hours
Prerequisites
Topology, basics on differential geometry of surfaces and of complex analysis in one variable.
Learning outcomes
We would like to give the basic notions of the theory of Riemann surfaces and complex algebraic curves. We will explain some of the techniques used in their study such as divisors, line bundles, sheaves and cohomology.
Course contents
Riemann surfaces. Abelian differentials. Divisors, meromorphic functions, meromorphic forms and linear systems. Sheaves and their cohomology. Algebraic curves and Riemann Roch theorem. The Jacobian of a curve. Abel's theorem.
Teaching methods
Lectures.
Reccomended or required readings
1. Rick Miranda: “Algebraic Curves and Riemann Surfaces”, American Mathematical Society.
2. Otto Forster: "Lectures on Riemann Surfaces", Springer.
3. Raghavan Narasimhan: "Compact Riemann Surfaces", Birkhaeuser.
Assessment methods
Oral exam.
We will verify both the knowledge of the theory and the ability to solve problems and exercises.
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