  Let X be a projective manifold, and let H be the associated small phase
space; this is a Frobenius manifold with canonical choice of fundamental
solution for the Dubrovin connection. The large phase space of X may be
identified with the jet-space of curves in H.
  In this paper, we formulate the differential equations satisfied by the
higher-genus potentials F_g of X, such as topological recursion relations and
the Virasoro constraints, in an intrinsic fashion on the jet space of H, that
is, in such a way that the equations do not depend on the choice of fundamental
solution. This effort is rewarded by a closer relationship between the
resulting theory and the geometry of moduli spaces of stable curves.
  A consequence of our analysis is the proof of a conjecture of Eguchi and
Xiong: F_g is a function on the jet space of jets of order 3g-2.
