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We prove that a blowing-up formula for the intersection cohomology of themoduli space of rank 2 Higgs bundles over a curve with trivial determinantholds. As an application, we derive the Poincar\'{e} polynomial of theintersection cohomology of the moduli space under a technical assumption.

A blowing-up formula for the intersection cohomology of the moduli of rank 2 Higgs bundles over a curve with trivial determinant