Abstract
Generalizing the ideas in [14] and using virtual Hodge polynomials as well as tours actions, we compute the Euler characteristics of certain moduli spaces of 1-dimensional closed sub-schemes when the ambient smooth projective variety admits a Zariski-locally trivial fibration to a codimension-1 base. As a consequence, we partially verify a conjecture of W.-P. Li and Qin [14]. We also calculate the generating function for the number of certain punctual 3-dimensional partitions, which is used to compute the above Euler characteristics.