The E-polynomial for the intersection cohomology of the moduli space of Higgs bundles

Let $C$ be a smooth projective curve of genus $g\geq2$. Following a method by O' Grady, construct a desingularization $\hat{\mathcal{M}}_{Dol}$ of the moduli space $\mathcal{M}_{Dol}$ of semistable Higgs bundles $(V,\Phi)$ with trivial determinant on $C$. For $g=2$ we prove that $\hat{\mathcal{M}}_{Dol}$ can be blown down to another desingularization $\tilde{\mathcal{M}}_{Dol}$ which is semismall and use the decomposition theorem by Beilinson, Bernstein, Deligne and Gabber to compute the E-polynomial for the intersection cohomology of $\mathcal{M}_{Dol}$.