In this paper, we study a variation in a conjecture of Debarre on positivity of cotangent bundles of complete intersections. We establish the ampleness of Schur powers of cotangent bundles of generic complete intersections in projective manifolds, with high enough explicit codimension and multi-degrees. Our approach is naturally formulated in terms of flag bundles and allows one to reach the optimal codimension. On complex manifolds, this ampleness property implies intermediate hyperbolic properties. We give a natural application of our main result in this context.

中文翻译：

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余切束的Schur幂和k-双曲率

在本文中，我们研究了Debarre猜想关于完全相交的切向束的正性的变化。我们建立了射影流形中具有足够高的显式维数和多度数的泛型完备交集的余切束的Schur幂的充分性。我们的方法自然是根据标志束来制定的，并允许其达到最佳余量。在复杂流形上，此充裕度特性表示中等双曲率特性。在这种情况下，我们自然地应用了我们的主要结果。