论文标题
通用矢量束，推向前向公式和特征形式的积极性
Universal vector bundles, push-forward formulae and positivity of characteristic forms
论文作者
论文摘要
鉴于在复杂的歧管上有一个冬粒溶性载体束，因此将其旗帜捆绑在诱导指标的相关通用矢量捆绑中。我们证明，在所有可能的通用矢量束的Chern类中，多项式推动的通用公式在Chern形式的水平上也保持点状。我们证明的一个关键步骤是，在任何标志束的点上，具有诱导指标的通用向量束的Chern曲率的明确计算。作为一个应用程序，我们在差异形式的级别上提供了Jacobi-Trudi身份的替代版本。我们还显示了格里菲斯（Griffiths）半阳性矢量束的多项式家族的积极性。后一个结果部分证实了格里菲斯对积极特征形式的猜想，这在近年来引起了极大的兴趣。
Given a Hermitian holomorphic vector bundle over a complex manifold, consider its flag bundles with the associated universal vector bundles endowed with the induced metrics. We prove that the universal formula for the push-forward of a polynomial in the Chern classes of all the possible universal vector bundles also holds pointwise at the level of Chern forms. A key step in our proof is the explicit computation, at a point of any flag bundle, of the Chern curvature of the universal vector bundles with the induced metrics. As an application, we provide an alternative version of the Jacobi-Trudi identity at the level of differential forms. We also show the positivity of a family of polynomials in the Chern forms of Griffiths semipositive vector bundles. This latter result partially confirms the Griffiths' conjecture on positive characteristic forms, which has raised considerable interest in recent years.
