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The choice of a Poincar\\'e bundle for such a moduli space $M$ induces an isomorphism between $X$ and a component of the moduli space of semistable sheaves over $M$. We prove that $h^0(M, \\text{End}({\\mathcal E})\\otimes TM)= 1$ for a vector bundle $\\mathcal E$ on $M$ coming from this component. 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