Mathematisches Institut der Universität Bonn

Arbeitsgruppe Komplexe Geometrie
Lehrveranstaltungen Prof. Dr. Daniel Huybrechts
im Wintersemester 2009/2010:

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Algebraic Geometry III (Modul V5A4)

Montag 10:00 ct- 12:00 Uhr; SR 11
Freitag 10:00 ct - 12:00 Uhr; SR 11

The course will be an introduction to some of the fundamental techniques in algebraic geometry. I will explain the construction of Grothendieck's Quot scheme and of the Hilbert and Picard scheme.
In the first part I will provide the necessary background on flat, smooth and étale morphisms. This is a natural continuation of my course on algebraic geometry and requires knowledge of schemes and cohomology.

References:

R. Hartshorne, Algebraic Geometry, Springer, GTM 52, 1977
A. Grothendieck: Fondements de la géométrie algébrique. [Extraits du Séminaire Bourbaki, 1957-1962.] Secrétariat mathématique, Paris 1962.
B. Fantechi et al: Fundamental Algebraic Geometry. Grothendieck's FGA Explained. AMS Math. Surveys and Monographs 123. 2005

More references will be given in class.

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Graduate Seminar on Differential Geometry (Modul S4D1)
Complex Geometry

Freitag, 12:00 ct - 14:00 Uhr; SR 11

The seminar, which will be organized more like a reading class with participants asked to present material not only at one occasion, will cover parts of the theory contained in [1]-[3]. (The references [4]-[6] are more advanced and can be used to go deeper into the subject.) The seminar will be concerned with the global aspects of the theory of compact complex manifolds. We will discuss basic notions for holomorphic functions in several variables (eg the Weierstrass preparation theorem), but will only quote the deeper analytical aspects of the theory. We will emphasize the geometric concepts and cohomoloigcal methods in the study of compact complex manifolds.

The seminar will naturally split into three parts:

I. Local Theory (Holomorphic variables and differential forms).

II. Complex manifolds and holomorphic vector bundles

III. Kähler manifolds (Kähler identities and Hodge theory).

Details

For further information please contact Heinrich Hartmann (hartmann@math.uni-bonn.de) or me (huybrech@math.uni-bonn.de).
Please have a look at Chapter 1 in [3] and let us know which of the basic material is already familiar to you.

References:

[1] W. Ballmann: Lectures on Kähler manifolds. ESI Lectures in Mathematics and Physics. EMS, Zürich, 2006

[2] M. de Cataldo: The Hodge theory of projective manifolds. Imperial College Press, London, 2007

[3] D. Huybrechts: Complex geometry. An introduction. Universitext. Springer-Verlag, Berlin, 2005

[4] C. Voisin: Hodge theory and complex algebraic geometry. I. Cambridge Studies in Advanced Mathematics, 76. 2002

[5] Ph. Griffiths, J. Harris: Principles of algebraic geometry. John Wiley & Sons, Inc., New York, 1978

[6] J.-P. Demailly Complex differential geometry. http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf

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Graduate Seminar on Algebraic Geometry (Modul S4A2)
Seminar on 'Noether Lefschetz and Gromov-Witten theory'
SFB-Seminar Transregio 45

Dienstag 14:00 ct - 18:00 Uhr; SR 11

Termine: 27. Oct.; 10. Nov.; 24. Nov., 08. Dec.; 19. Jan.; 02. Feb.

Details

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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.

Details: SAG WS 2009/10

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Last modified: 07/2009
sachinid (in domain math.uni-bonn.de)