Arbeitsgruppe Komplexe Geometrie (Prof. Dr. Daniel Huybrechts)
Veranstaltungen im WS 06/07:
Vorlesung Lineare Algebra I
Dienstag 08.00 ct- 10.00 Uhr, Freitag 10.00 ct - 12.00 Uhr, Wolfgang-Paul HS
Die Lineare Algebra gehört zu den Fundamenten der Mathematik.
Behandelt werde u.a. folgende Themenkreise:
Lineare Gleichungssysteme, Vektorräume, Lineare Abbildungen, Determinanten, Eigenwerte, Normalformen
Übungen: Dr. Eva Viehmann
vgl. Übungen zur Vorlesung Lineare Algebra I
Literatur:
Falko Lorenz: Lineare Algebra, 4. Auflage, Spektrum Akademischer Verlag GmbH,
Heidelberg, Berlin
Weitere Empfehlungen in der Vorlesung
Studentenseminar zur Algebraischen Geometrie
Thema: Korrespondenzen, Motive und Standardvermutungen
Freitag, 12.00 ct - 14.00 Uhr, SR A
Ziel des Seminars wird es sein, Appendix A in Hartshorns Buch
'Algebraic Geometry' zu verstehen,
d.h. wir werden uns mit Dingen,wie der Grothendieckschen K-Gruppe,
Chernklassen und der Formel von Riemann-Roch in der Grothendieckschen Fassung, etc. beschäftigen.
Vorkenntnisse aus der Algebraischen Geometrie sind erforderlich, die Vorlesung des SS (J. Stix) genügt sicherlich.
Grundlage des Seminars ist die Arbeit:
Manin, Yu. I.: Lectures on de K-functor in algebraic geometiry (Russ. oder Englisch)
Wenn möglich, werden wir auch noch etwas über Chow-Gruppen lernen, z.B. aus dem Buch
Fulton W.: Intersection Theory.
Anmeldung zur Teilnahme bei Sven Meinhardt (sven at math.uni-bonn.de,
Be4/Z 34) oder mir.
Oberseminar zur Komplexen Geometrie
Dienstag, 12.00 ct - 14.00 Uhr, SR A
Start October 17
This semester (and maybe the next one as well) we will work through
large parts of the books of Lazarsfeld.
Some more details and a few thoughts on how to run the seminar:
The title of the book refers to positivity as we all know it from
basic courses in algebraic geometry; ampleness of a line bundle.
It is amazing to see, however, how little we actually understand
in specific situations. There are global aspects and less
well-known local ones. The latter are encoded by the Seshadri
constant, a good geometric understanding of which I could see as
the goal for the first term.
The aim of the seminar is not to work up to one big theorem, but
rather to learn as many of the important techniques in the area as
possible. So, the focus will be on techniques and examples,
although we will see quite a number of beautiful theorems on the
way. For the first term I would propose to concentrate on Chapter
1,2, and 5 in volume I. (So, we would leave out Chapter 3 which
deals with Lefschetz type results and Chapter 4 on vanishing
theorems, which were discussed in some length already in my
lectures last year.)
The character of the seminar will be more that of a reading class.
We will be free to skip topics and to follow some of the many
ramifications proposed by the text but which are not covered in
detail. In particular, some of the application, eg to moduli
spaces of curves, abelian varieties, etc, could be of interest.
I think volume II is much harder, but without having worked
through the many examples in volume I, it will be impossible to
get a good feeling for the geometry. In the same spirit, I would
propose to take the time, if you want as a warm-up, to review some
of the basic material in Chapter 1 (which certainly also contains
material less familiar). How fast we proceed depends on us.
Literatur:
R. Lazarsfeld Positivity in Algebraic Geometry I&II Springer
Seminar Algebraische Geometrie (SAG)
Donnerstag, 10.30 Uhr Hörsaal MPI, Vivatsgasse 7
Vorträge zu aktuellen Ergebnissen der algebraischen und komplexen Geometrie.
Programm vlg.
Last modified:
18.10.2006 sachinid (in domain math.uni-bonn.de)
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