Let M_H(c₁,c₂) be the moduli of H-stable sheaves on a surface X. For a divisor D on X, we can associate a determinant line bundle whose first chern class is defined by the μ-map. I consider the Euler characteristic of this determinant line bundle.In particular, I will talk about the wall crossing formula under a suitable assumption on X. This is a joint work with Lothar Goettsche and Hiraku Nakajima.