论文标题
关于足够的矢量束的高度Schur类的积极性
On the positivity of high-degree Schur classes of an ample vector bundle
论文作者
论文摘要
让$ x $成为尺寸$ n $的光滑投射品种，让$ e $成为超过$ x $的足够的矢量捆绑包。我们表明，任何非零的Schur类别的$ e $，位于同居小组的Bidegree $（N-1，N-1）$中，都有一个代表，这在平滑形式的意义上是严格积极的。这构成了格里菲斯对Chern类别的正多项式的预测，形式级别上有足够的矢量束，从而增强了富尔顿·拉扎尔斯菲尔德（Fulton Lazarsfeld）的著名阳性结果。
Let $X$ be a smooth projective variety of dimension $n$, and let $E$ be an ample vector bundle over $X$. We show that any non-zero Schur class of $E$, lying in the cohomology group of bidegree $(n-1, n-1)$, has a representative which is strictly positive in the sense of smooth forms. This conforms the prediction of Griffiths conjecture on the positive polynomials of Chern classes/forms of an ample vector bundle on the form level, and thus strengthens the celebrated positivity results of Fulton-Lazarsfeld for certain degrees.
