论文标题
在正面矢量束的特征形式，混合判别和推动身份
On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities
论文作者
论文摘要
我们证明，中nakano的Chern形式和双中nakano阳性矢量束的schur多项式是差异形式的阳性。此外，Modulo关于线性算子在矩阵上的“双重混合判别”的阳性（以保留正定矩阵的锥体的阳性）的阳性，我们确定以chern形式的Griffiths阳性矢量捆绑包中的schur多项式是弱阳性的。这为富尔顿·拉扎尔斯菲尔德（Fulton Lazarsfeld）的不平等不平等提供了微分几何版本。通过操作员理论对矢量束的阳性条件的解释是我们方法的核心。我们证明的另一个重要步骤是为特征形式建立一定的推动身份，并在差异形式的层面上精炼了kempf-laksov的决定性公式。同样，我们建立了雅各比 - 特鲁迪身份的本地版本。然后，我们研究了逆问题，并表明已经在复杂表面上的向量捆绑包中已经无法通过Schur多项式的阳性来表征Griffiths的积极性（甚至是增强性），即使人们会考虑所有Vector Bundle的载体。
We prove that Schur polynomials in Chern forms of Nakano and dual Nakano positive vector bundles are positive as differential forms. Moreover, modulo a statement about the positivity of a "double mixed discriminant" of linear operators on matrices, which preserve the cone of positive definite matrices, we establish that Schur polynomials in Chern forms of Griffiths positive vector bundles are weakly-positive as differential forms. This provides differential-geometric versions of Fulton-Lazarsfeld inequalities for ample vector bundles.An interpretation of positivity conditions for vector bundles through operator theory is in the core of our approach. Another important step in our proof is to establish a certain pushforward identity for characteristic forms, refining the determinantal formula of Kempf-Laksov for homolorphic vector bundles on the level of differential forms. In the same vein, we establish a local version of Jacobi-Trudi identity.Then we study the inverse problem and show that already for vector bundles over complex surfaces, one cannot characterize Griffiths positivity (and even ampleness) through the positivity of Schur polynomials, even if one takes into consideration all quotients of a vector bundle.
