ALGEBRAIC CURVES AND RIEMANN SURFACES
Stampa
Enrollment year
2022/2023
Academic year
2022/2023
Regulations
DM270
Academic discipline
MAT/03 (GEOMETRY)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Course
MATHEMATICS
Curriculum
PERCORSO COMUNE
Year of study
Period
2nd semester (01/03/2023 - 09/06/2023)
ECTS
6
Lesson hours
48 lesson hours
Language
Italian
Activity type
ORAL TEST
Teacher
PIROLA GIAN PIETRO (titolare) - 6 ECTS
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
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 and Torelli theorem.
Projective structures.
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.
4. Gunning, R. C. Lectures on Riemann surfaces. Princeton Mathematical Notes Princeton University Press, Princeton, N.J. 1966
Assessment methods
Oral exam.
We will verify both the knowledge of the theory and the ability to solve
problems and exercises.
Further information
Sustainable development goals - Agenda 2030