论文标题
感谢
Toric sheaves, stability and fibrations
论文作者
论文摘要
对于在两极分化的复曲面上进行的反射式捆，我们研究了其反射性回溯沿着曲曲面纤维的斜率稳定性。此类纤维化的例子包括模棱两可的爆破和图火局部琐碎的纤维。我们表明，在这样的绝热极性化的此类撤回下，保留了稳定性（不稳定）。在严格的半标准情况下，在当地的假设下，我们在分级对象上提供了必要且充分的条件，以确保拉回捆的稳定性。作为应用，我们通过改变极化或通过炸毁亚物种来提供各种可半固定的切线束的稳定扰动。最后，我们的结果均匀地适用于特定的平坦家族，并诱导相关模量空间之间的注射图。
For an equivariant reflexive sheaf over a polarised toric variety, we study slope stability of its reflexive pullback along a toric fibration. Examples of such fibrations include equivariant blow-ups and toric locally trivial fibrations. We show that stability (resp. unstability) is preserved under such pullbacks for so-called adiabatic polarisations. In the strictly semistable situation, under locally freeness assumptions, we provide a necessary and sufficient condition on the graded object to ensure stability of the pulled back sheaf. As applications, we provide various stable perturbations of semistable tangent sheaves, either by changing the polarisation, or by blowing-up a subvariety. Finally, our results apply uniformly in specific flat families and induce injective maps between the associated moduli spaces.
