Mathematical Institute of the University of Bonn

Arbeitsgruppe Komplexe Geometrie
Lehrveranstaltungen Prof. Dr. Daniel Huybrechts u. AG Komplexe Geometrie
im Sommersemester 2013:

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Vorlesung Algebraic Geometry III: K3 surfaces (V5A3)
D. Huybrechts

Montag 10:00 ct - 12:00 Uhr, Endenicher Allee 60, Seminarraum 0.011
Freitag 10:00 ct - 12:00 Uhr, Endenicher Allee 60, Seminarraum 0.011

This course will cover basic aspects of the theory of K3 surfaces and, at the same time, introduce important techniques in algebraic geometry. For the first parts I will rely on the lecture notes here:

Details

Later I will try to cover further topics, eg derived categories of coherent sheaves on K3 surfaces, automorphism groups of K3 surfaces, etc. Some fair amount of lattice theory will have to be discussed as we go along.

A solid background in algebraic geometry will be assumed, eg Liedtke's course last semester or Hartshorne's book.

References:

R. Hartshorne, Algebraic Geometry, Springer, GTM 52, 1977; tba

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Graduate Seminar on Algebraic Geometry (S4A1):
Fano varieties and cubics: Hodge theory and derived categories
D. Huybrechts

Dienstag 14:00 ct - 18:00 Uhr, Endenicher Allee 60, Seminarraum 0.011 bzw. Lipschitzsaal

Details

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Graduate Seminar on Advanced Geometry (Modul S4D3):
D. Huybrechts u. T. Schuerg

Donnerstag, 14:00 ct - 16:00 Uhr, Endenicher Allee 60, Seminarraum 0.011

The seminar 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.

Further Details

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 (SAG) (Modul S4A2)
Gastvorträge zu aktuellen Ergebnissen der algebraischen und komplexen Geometrie

Donnerstag 10.30 Uhr, Hörsaal MPI, Vivatsgasse 7

SAG Sommersemester 2013

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Last modified: 03/2013
sachinid (in domain math.uni-bonn.de)