  Starting from the candidate Bloch-Beilinson filtration on Chow groups of
0-cycles constructed by J. Lewis, we develop and describe geometrically a
series of Hodge-theoretic invariants defined on the graded pieces. Explicit
formulas (in terms of currents and membrane integrals) are given for certain
quotients of the invariants, with applications to 0-cycles on products of
curves.
