ALGEBRAIC FIBER SPACES AND CURVATURE OF HIGHER DIRECT IMAGES
ALGEBRAIC FIBER SPACES AND CURVATURE OF HIGHER DIRECT IMAGES
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DOI：
10.1017/s147474802000050x
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发表时间：
2017-04
影响因子：
0.9
通讯作者：
B. Berndtsson;Mihai Paun;Xu Wang
中科院分区：
文献类型：
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作者：
B. Berndtsson;Mihai Paun;Xu Wang
设$p：X\rightarrow Y$是代数纤维空间，$L$是X$上的线丛.本文得到了$\unicode[STIX]{x1 D 6 FA}_{X/Y}^{i}\otimes L$限制在$X$的一个适当的Zebrski开子集上的高阶直像的曲率公式.我们的结果是特别有意义的，如果$L$是半负弯曲的$X$和严格负的或平凡的光滑纤维的$p$。得到了几个应用，包括一个新的证明的结果Viehweg-Zuo的上下文中的一个典型的极化家庭的最大变化和它的版本的Calabi-Yau家庭。我们的方法的主要特点是，我们得到的一般曲率公式允许我们绕过使用分歧覆盖-和由它们引起的并发症。
Abstract Let $p:X\rightarrow Y$ be an algebraic fiber space, and let $L$ be a line bundle on $X$ . In this article, we obtain a curvature formula for the higher direct images of $\unicode[STIX]{x1D6FA}_{X/Y}^{i}\otimes L$ restricted to a suitable Zariski open subset of $X$ . Our results are particularly meaningful if $L$ is semi-negatively curved on $X$ and strictly negative or trivial on smooth fibers of $p$ . Several applications are obtained, including a new proof of a result by Viehweg–Zuo in the context of a canonically polarized family of maximal variation and its version for Calabi–Yau families. The main feature of our approach is that the general curvature formulas we obtain allow us to bypass the use of ramified covers – and the complications that are induced by them.