Program:

• Binary forms and their geometric invariant theory, other examples of group actions.
• Bundles on P^1, bundles on P^n and minimal resolutions, jumping lines of first and second order, jumping conics.
• Maruyama moduli scheme of semistable bundles, local and global properties.
• The Euler sequence, nullcorrelation and logarithmic bundles Steiner bundles and multidimensional matrices.
• Hyperdeterminants and nondegenerate matrices, their geometric invariant theory and examples.
• Schwarzenberger bundles. Poncelet type theorems. Barth morphism.
• Exceptional bundles and helixes. Theorem of Drezet - Le Potier.

Book references:

• Gelfand I.M., Kapranov M.M. , Zelevinsky A.V., Discriminants, Resultants and Multidimensional Determinants, Birkhauser, 1994.
• Harris J, Algebraic geometry, A first course, Springer 1992
• Huybrechts, D. Lehn M., The geometry of moduli spaces of sheaves. Vieweg 1997.0
• Le Potier J., Lectures on vector bundles, Cambridge Studies in Advanced Mathematics, 54, Cambridge University Press (specially chap. 6 by C. Sorger)
• Newstead P., Introduction to moduli problems and orbit spaces, Tata institute.
• Okonek C., Schneider M., Spindler H., Vector bundles on complex projective spaces, Birkauser 1980.

The school took place in a pension Gawra located on a lake in woods near village Wykno, about 150 km North from Warsaw.

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).