Universiteit Faculteit FNWI English version | 3 november 2003, e-mail |

## Woensdag 5 november 2003
Vanaf half 11 is er koffie en chocola.
## AbstractA linear arrangement is a finite set of linear hyperplanes in a finite dimensional complex vector spaceV.
For "special" arrangements the hyperplane complement can be endowed with
a differential equation of hypergeometric type, and the goal of this lecture is
to explain a criterion (in terms of exponents) for the solutions to yield
a constant curvature geometry on the projective space P(V),
possibly properly modified.
The basic example of a "special" arrangement is the braid arrangement, which is the arrangement of mirrors of the symmetric group in the reflection representation space. The case of the symmetric group on 3 letters corresponds to the case of the Gauss hypergeometric equation, and the above mentioned criterion was given by H.A. Schwarz. After a review of this very classical (and beautiful) work the plan is to explain how and why the Schwarz condition also shows up in the multivariable setting. |