  The goal of this paper is to give a geometric construction of the Bethe
algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra.
More precisely, in this paper a quantum integrable model is assigned to a
weighted arrangement of affine hyperplanes. We show (under certain assumptions)
that the algebra of Hamiltonians of the model is isomorphic to the algebra of
functions on the critical set of the corresponding master function. For a
discriminantal arrangement we show (under certain assumptions) that the
symmetric part of the algebra of Hamiltonians is isomorphic to the Bethe
algebra of the corresponding Gaudin model. It is expected that this
correspondence holds in general (without the assumptions). As a byproduct of
constructions we show that in a Gaudin model (associated to an arbitrary simple
Lie algebra), the Bethe vector, corresponding to an isolated critical point of
the master function, is nonzero.
