We study the geometrical meaning of the Faa' di Bruno polynomials in the
context of KP theory. They provide a basis in a subspace W of the universal
Grassmannian associated to the KP hierarchy. When W comes from geometrical data
via the Krichever map, the Faa' di Bruno recursion relation turns out to be the
cocycle condition for (the Welters hypercohomology group describing) the
deformations of the dynamical line bundle on the spectral curve together with
the meromorphic sections which give rise to the Krichever map. Starting from
this, one sees that the whole KP hierarchy has a similar cohomological meaning.Comment: 16 pages, LaTex using amssymb.sty. To be published in Lett. Math.
Phy
