Wall-crossing formulae for algebraic surfaces with $q>0$

Abstract

We extend the ideas of Friedman and Qin (Flips of moduli spaces and transition formulae for Donaldson polynomial invariants of rational surfaces) to find the wall-crossing formulae for the Donaldson invariants of algebraic surfaces with geometrical genus zero, positive irregularity and anticanonical divisor effective, for any wall $\zeta$ with $l_{\zeta}=(\zeta\sp{2}-p_1)/4$ being zero or one.