25th Autumn School in Algebraic Geometry

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

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

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

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.


  • 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).

  • September Schools Homepage
  • Polish Eager Homepage