标题： Baily--Borel 间隔的周期图像和 b-半放大猜想 显示英文标题

标题： Baily--Borel compactifications of period images and the b-semiampleness conjecture

摘要： 我们解决与从Hodge理论中出现的线丛的半幅性质相关的两个问题。 首先，我们证明了极化整纯Hodge结构的周期映射像存在一个函子性紧化，使得Griffiths丛可以充分扩展。 特别是，Griffiths丛是半幅的。 我们更一般地证明了Calabi--Yau Hodge结构的Hodge丛在一些额外条件下的半幅性质，并作为我们的第二个结果推导出Prokhorov--Shokurov的b-半幅猜想。 半幅性质结果（以及Baily--Borel紧化的构造）关键地使用了o-极小GAGA，而对b-半幅猜想的推导使用了Ambro的工作和Kollár关于最小lc中心几何的结果来验证额外条件。 显示英文摘要

摘要： We address two questions related to the semiampleness of line bundles arising from Hodge theory. First, we prove there is a functorial compactification of the image of a period map of a polarizable integral pure variation of Hodge structures for which the Griffiths bundle extends amply. In particular the Griffiths bundle is semiample. We prove more generally that the Hodge bundle of a Calabi--Yau variation of Hodge structures is semiample subject to some extra conditions, and as our second result deduce the b-semiampleness conjecture of Prokhorov--Shokurov. The semiampleness results (and the construction of the Baily--Borel compactifications) crucially use o-minimal GAGA, and the deduction of the b-semiampleness conjecture uses work of Ambro and results of Koll\'ar on the geometry of minimal lc centers to verify the extra conditions.