We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We then proceed to describe the surface itself as a moduli space of rank two vector bundles on it. Lastly, we give a proof of the Bogomolov inequality for semistable rank two sheaves on integral surfaces in three-dimensional projective space in all characteristics.

中文翻译：

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在某些一般类型的表面上稳定第二级滑轮的判别式

我们证明了三维投影空间中曲面上的稳定秩为2的滑轮的判别上的尖锐边界。关键技术要素是通过派生类别中的倾斜稳定性将它们作为投射空间中的扭力滑轮进行研究。然后，我们将表面本身描述为其上的秩为2的矢量束的模空间。最后，我们给出了在所有性质的三维投影空间中积分表面上的半稳定二级滑轮的Bogomolov不等式的证明。