  The paper is a part of our program to build up a theory of couting immersed
nodal curve on algebraic surfaces, as an enumerative Riemann-Roch theory
(outlined in math.AG/0405113). In this paper, we discuss the excess
intersection theory of the so-called type two exceptional curves, which plays
the analogous role as the "index of speciality" (h^2) in the classical surface
Riemann-Roch formula.
  We show that the algebraic family Seiberg-Witten theory of type I exceptional
curves can be generalized to the theory of type II exceptional curves when the
family moduli spaces are not regular of the expected dimension.
