  Mcduff had proposed in 1997 a way to modify the definition of Taubes' version
of Gromov invariant when multiple coverings of -1 curves appear. In this paper
we generalize Mcduff's proposal to the family case, as is needed in the
discussion of family Seiberg-Witten theory. For simplicity, the discussion has
been formulated in the algebraic category.
