Arbeitsgruppe Komplexe Geometrie
Lehrveranstaltungen Prof. Dr. Daniel Huybrechts
im Sommersemester 2009:

Vorlesung Algebraic Geometry II (Modul V4A2)

Dienstag 08:00 ct- 10:00 Uhr Zeichensaal Wegelerstr. 10,
Freitag 10:00 ct - 12:00 Uhr, ab 08.05.09 freitags in LWK 011!

This is part two of the general introduction into the basic principles of algebraic geometry. In the first weeks we will introduce more basic properties of schemes and morphisms (eg. proper, separated). Then we will develop the general machinery of derived categories and derived functors. This will then enable us to speak about cohomology of quasi-coherent sheaves.
We will partially follow Hartshorne's book [Ha]. The homological algebra will be developed more abstractly however and will use other sources. The aim of this second part is to cover the remaining sections of Chapter 2 and the whole Chapter 3 in [Ha]. If time permits, we will prove the Riemann-Roch formula for curves.

Literatur:
[Ha] R. Hartshorne, Algebraic Geometry, Springer, GTM 52, 1977
[L] Q. Liu, Algebraic Geometry and Arithmetic Curves
[M] D. Mumford, The Red Book of Varieties and Schemes, Springer, Lecture Notes 1358, 1999

Organisation der Übungen und Übungsblätter: Dr. Sören Rollenske

Graduate Seminar on Algebra (Modul S4A1)
Advanced topics in Hodge theory and Chow groups of algebraic varieties

Freitag, 12:00 ct - 14:00 Uhr, SR A (LWK 107)

This seminar is a continuation of last terms seminar but technically rather independent of it. We will follow [V] and work through Chapter 21-23. (This corresponds to III.9-11 in Vol 2 of the english translation.) We will start with the definition of Chow groups and their basic properties. For more details we use [F]. The aim of the seminar is to understand Mumford's theorem saying that under certain cohomological conditions on the variety, the Chow group is of infinite dimension. The last part treats geometric aspects of the Bloch conjecture which predicts the existence of a natural filtration of the Chow ring whose graded pieces are governed by the more transcendental parts of cohomology. The seminar should be accessible to everyone with a sound knowledge of algebraic geometry. Later in the seminar we will use the Hodge theoretic aspects introduced last term (which one might accept as a black box).

Literatur:
[F] W. Fulton Intersection theory. Springer
[V] C. Voisin, Théorie de Hodge et géométrie algébrique complexe (or the english translation published by Cambridge)

Detailed plan

Graduate Seminar on Algebraic Geometry (Modul S4A2)
Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
(after Kontsevich and Soibelman)

Dienstag 14:00 ct - 18:00 Uhr, Raum 11, Endenicher Allee 60
Termine: 28.04. (Bonn), 12.05. (Bonn), 26.05. (Mainz), 09.06., 23.06., 07.07.

Detailed plan

Graduate Seminar on Algebraic Geometry (SAG) (Modul S4A2)

Donnerstag, 10.30 Uhr Hörsaal MPI, Vivatsgasse 7

Vorträge zu aktuellen Ergebnissen der algebraischen und komplexen Geometrie. Programm vgl. SAG SS 2009