论文标题
用庞加莱型扭曲的直接图像的积极性
Positivity of direct images with a Poincaré type twist
论文作者
论文摘要
我们考虑一个全态家族$ f：\ mathcal {x} \ to compact复合歧管的s $和line Bundle $ \ MATHCAL {l} \ to \ MATHCAL {x} $。鉴于$ \ Mathcal {l}^{ - 1} $带有一个奇异的Hermitian度量标准，该指标沿相对Snc Divisor $ \ Mathcal {D} $具有Poincaré类型的奇异性，直接image $ f _**（k _ {k _ {\ nathcal {\ nathcal {x}/s}}/s}}/s}/s}/s} \ Mathcal {l}）$带有光滑的Hermitian度量。如果$ \ Mathcal {l} $相对积极，我们为其曲率提供明确的公式。该结果适用于对数 - 共偏振对的家族。此外，我们表明，在大型捆绑包的特殊情况下，它改善了Berndtsson-Păun的总体积极性结果。
We consider a holomorphic family $f:\mathcal{X} \to S$ of compact complex manifolds and a line bundle $\mathcal{L}\to \mathcal{X}$. Given that $\mathcal{L}^{-1}$ carries a singular hermitian metric that has Poincaré type singularities along a relative snc divisor $\mathcal{D}$, the direct image $f_*(K_{\mathcal{X}/S}\otimes \mathcal{D} \otimes \mathcal{L})$ carries a smooth hermitian metric. In case $\mathcal{L}$ is relatively positive, we give an explicit formula for its curvature. The result applies to families of log-canonically polarized pairs. Moreover we show that it improves the general positivity result of Berndtsson-Păun in a special situation of a big line bundle.
