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25th Autumn School in Algebraic Geometry

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Vector bundles over curves and higher dimensional varieties, and their
moduli

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Lukecin, Poland, September 8th - September 15th, 2002

**Teachers:** Peter Newstead (Liverpool) and Adrian Langer (Warszawa)
**Program:**

*Newstead's lectures:* Geometric Invariant Theory. Construction of
moduli spaces following Simpson. Topology of moduli spaces of vector bundles
on curves. Geometry I: Irreducibility, rationality, projective embeddings,
Verlinde formulae. Geometry II: Torelli theorems, maximal subbundles,
Brill-Noether theory.

*Langer's lectures: *Bogomolov's instability and
restriction theorems. Results of Gieseker, Li and O'Grady on moduli spaces
of semistable sheaves on surfaces. Determinantal line bundles and Le
Potier's strange duality.

**Notes**

Adrian Langer:* Moduli Spaces of Sheaves on Higher Dimensional
Varieties*
Peter Newstead: *Vector Bundles on Algebraic Curves*
**Further Readings:**

D. Huybrechts, M. Lehn: * The geometry of moduli spaces of
sheaves.* Aspects of Mathematics, E31. Friedr. Vieweg & Sohn,
Braunschweig.
P. Newstead: *Introduction to moduli problems and orbit spaces.*
Tata Institute of Fundamental Research Lectures on Mathematics and Physics,
51. Tata Institute of Fundamental Research, Bombay.
J. Le Potier, *Lectures on vector bundles.* Cambridge Studies in
Advanced Mathematics, 54. Cambridge University Press, Cambridge.

A joint picture of all participants

The school was financially supported by Institute of Mathematics
of Warsaw University, as well as by Polish State Committee for Scientific
Research and EAGER (European Algebraic Geometry Research Training
Network, EC contract HPRN-CT-200-00099).

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