论文标题
较高维度的Arakelov不平等现象
Arakelov inequalities in higher dimensions
论文作者
论文摘要
我们为投射流形的家族开发了一个杂货理论不变，该家族在较高的维度中衡量了阿拉克洛夫型不平等的潜在失败，这种不平等现象自然而然地概括了经典的阿拉克洛夫不平等，而不是常规的准标准曲线。我们表明，对于有足够的典型束的多种流形的家庭，这种不变的界限是统一的。结果，我们确定在任意维度基础上的此类家庭验证了上述的Arakelov不平等，回答了Viehweg的问题。
We develop a Hodge theoretic invariant for families of projective manifolds that measures the potential failure of an Arakelov-type inequality in higher dimensions, one that naturally generalizes the classical Arakelov inequality over regular quasi-projective curves. We show that for families of manifolds with ample canonical bundle this invariant is uniformly bounded. As a consequence we establish that such families over a base of arbitrary dimension verify the aforementioned Arakelov inequality, answering a question of Viehweg.
