In this paper, we study the Nakano-positivity and dual-Nakanopositivity of certain adjoint vector bundles associated to ample vector bundles. As applications, we get new vanishing theorems about ample vector bundles. For example, we prove that if E is an ample vector bundle over a compact K?hler manifold X, SkE O×p det E is both Nakano-positive and dual-Nakano-positive for any k ≤ 0. Moreover, Hn,q (X, S k E O× det E) = Hq,n(X, SkE O× det E) = 0 for any q ≤ 1. In particular, if (E, h) is a Griffiths-positive vector bundle, the naturally induced Hermitian vector bundle (SkE O× det E, Skh O× det h) is both Nakano-positive and dual-Nakano-positive for any k ≥ 0.
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机译：在本文中，我们研究了与足够的向量束相关的某些伴随向量束的中野正性和双重中野正性。作为应用程序，我们得到了关于大量矢量束的新的消失定理。例如，我们证明，如果E是紧致K？hler流形X上的足够大的向量束，则对于任何k≤0，SkE O×p det E既是Nakano正的，也是对偶Nakano正的。对于任何q≤1，（X，S k EO×de E）= Hq，n（X，SkE O×de E）=0。特别是，如果（E，h）是格里菲斯正矢量束，则自然诱导的埃尔米特向量束（SkE Ox det E，Skh Ox det h）在任何k≥0时都是Nakano正和双重Nakano正。
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