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$R^1\Gamma = 0$, and the Mumford stability
Let $S$ be a smooth projective surface with an ample divisor $H$ so that $K_S \cdot H < 0$.
Let us consider the Mumford slope $\mu(E) = \frac{H \cdot c_1(E)}{\operatorname{rk}(E)}$ on $\...
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