|Universiteit Faculteit FNWI English version||3 november 2003, e-mail|
Woensdag 5 november 2003
AbstractA linear arrangement is a finite set of linear hyperplanes in a finite dimensional complex vector space V. 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.