  We investigate the deformation theory of the simplest bihamiltonian structure
of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that
all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y.
Zhang, that is, trivial after allowing transformations where the first partial
derivative of the field is inverted. We reformulate the question about
deformations as a question about the cohomology of a certain double complex,
and calculate the appropriate cohomology group.
