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Seminar: An Introduction to Algebraic Curves / Compact Riemann Surfaces
| Dozent(in): |
Visiting Professor Dr. Emma Carberry |
| Termin: |
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| Gebäude/Raum: |
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| Ansprechpartner: |
Visiting Professor Dr. Emma Carberry |
Inhalt der Lehrveranstaltung:
This seminar will provide a geometric introduction to algebraic curves over the complex plane, which when they are smooth are also called compact Riemann surfaces. The two names reflect the fact that in this subject several branches of mathematics meet. The theory of algebraic curves is extremely rich and is important in its own right, but it also serves as a launching point both for algebraic geometry and for several complex variables. So here algebra needs analysis and geometry. We shall combine these viewpoints from the beginning.
We begin with an elementary introduction to algebraic curves and compact Riemann surfaces and explain how the two are related using the process of normalisation. Next semester we will continue with the crucial Riemann-Roch theorem and some of its many applications, and discuss the Jacobi variety, which in some sense provides a higher dimensional linearisation of a compact Riemann surface.
The first meeting will be on Thursday 6th December, 14:00, in room 1008 (L1) .
The seminar will consist of one lecture per week plus an additional hour in which we will discuss exercises and examples. The additional hour will be scheduled at the first meeting at a time convenient for the participants.
Literatur zur Lehrveranstaltung:
The text for this seminar is "Introduction to Algebraic Curves", by Philipp A. Griffiths. Some supplementary notes will also be provided.
weitere Informationen zu der Lehrveranstaltung:
| empfohlenes Studiensemester der Lehrveranstaltung: |
ab dem 5. Semester |
| Fachrichtung Lehrveranstaltung: |
Diplom-Mathematik |
| Nummer der Lehrveranstaltung: |
0 |
| Dauer der Lehrveranstaltung: |
keine Angabe |
| Typ der Lehrveranstaltung: |
S - Seminar |
| Bereich: |
Geometrie, Algebra |
| Semester: |
WS 2007/08 |
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