  A higher level analog of Weyl modules over multi-variable currents is
proposed. It is shown that the sum of their dual spaces form a commutative
algebra. The structure of these modules and the geometry of the projective
spectrum of this algebra is studied for the currents of dimension one and two.
Along the way we prove some particular cases of the conjectures in [FL1] and
propose a generalization of the notion of parking function representations.
