24rd Autumn School in Algebraic Geometry
Moduli of vector bundles and group action
Wykno (Poland), September 9  16, 2001
Teachers: Giorgio Ottaviani (Firenze, Italy) and Jean Valles
(Versailles  Saint Quentin en Yvelines, France).
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.
Prerequisites: basic knowledge of algebraic geometry (Hartshorne or
GriffithsHarris book), in particular sheaf cohomology. Previous
knowledge of vector bundles and their Chern classes will be useful.
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 HPRNCT20000099).
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