First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
RIEMANN SURFACES
SC01111818, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course First cycle degree in
MATHEMATICS
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2017/18
N0
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination RIEMANN SURFACES
Website of the academic structure http://matematica.scienze.unipd.it/2017/laurea
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge ERNESTO CARLO MISTRETTA MAT/03

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/03 Geometry 6.0

Mode of delivery (when and how)
Period Second semester
Year 3rd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Calendar
Start of activities 26/02/2018
End of activities 01/06/2018

Examination board
Board From To Members of the board
6 Superficie di Riemann - 2017/2018 01/10/2017 30/09/2018 MISTRETTA ERNESTO CARLO (Presidente)
BALDASSARRI FRANCESCO (Membro Effettivo)
BERTAPELLE ALESSANDRA (Supplente)
CAILOTTO MAURIZIO (Supplente)
CANDILERA MAURIZIO (Supplente)

Syllabus
Prerequisites: Algebra, geometry and analysis of the first two years. Basic knowledge on holomorphic functions of one variable.
Target skills and knowledge: The course aims to develop the fundamental concepts regarding compact Riemann surfaces (in particular, on spheres and tori), introducing the notion of genus and its interpretations (in particular, the Riemann-Roch theorem)
Examination methods: Written exam.
Assessment criteria: The exam test the acquired knowledge during the course and the capacity to apply this knowledge in particular cases.
Course unit contents: Introduction to the geometry of algebraic curves over the complex numbers. Topics

- Definition of a Riemann surface;
- Elementary properties of holomorphic functions on a Riemann surface;
- Detailed study of the Riemann sphere and tori;
- Divisors on compact Riemann surfaces; linear systems;
- Differential forms and Riemann-Roch theorem; applications;
- First notions of homology; Jacobians of Riemann surfaces and the Abel-Jacobi theorem;
Planned learning activities and teaching methods: Lectures and exercise classes
Textbooks (and optional supplementary readings)
  • Miranda Rick, Algebraic curves and Riemann Surfaces. --: AMS - GSM 5, 1995. (per consultazione) Cerca nel catalogo