论文标题
硬Lefschetz属性，完整的交叉点和数字维度
Hard Lefschetz properties, complete intersections and numerical dimensions
论文作者
论文摘要
我们研究了NEF类的完整交集的积极性。我们首先在完整的相交类中给出了足够的必要表征，这些类别在线性情况下等效地在紧凑的复合圆环上具有硬Lefschetz属性。反过来，这为我们提供了新型的共同体学类，这些类别在任意紧凑的Kähler歧管上具有Hodge-Riemann属性或Hard Lefschetz属性。我们还为何时在任意紧凑的Kähler歧管上进行完整的交叉点类给出了一个完整的表征。这两种特征均由给定NEF类的各个部分总和的数值维度给出。作为一个有趣的副产品，我们表明数值维度将任何有限的NEF类都带有无环性多肌膜结构。
We study the positivity of complete intersections of nef classes. We first give a sufficient and necessary characterization on the complete intersection classes which have hard Lefschetz property on a compact complex torus, equivalently, in the linear case. In turn, this provides us new kinds of cohomology classes which have Hodge-Riemann property or hard Lefschetz property on an arbitrary compact Kähler manifold. We also give a complete characterization on when the complete intersection classes are non-vanishing on an arbitrary compact Kähler manifold. Both characterizations are given by the numerical dimensions of various partial summations of the given nef classes. As an interesting byproduct, we show that the numerical dimension endows any finite set of nef classes with a loopless polymatroid structure.
