论文标题
混合周期图的图像的准注射率
Quasiprojectivity of images of mixed period maps
论文作者
论文摘要
我们证明了格里菲斯（Griffiths）的猜想的混合版本：任何可允许的混合周期图的图像的闭合是准主体，具有自然丰富的束。具体而言，我们考虑了从混合周期图的图像到相关分级的周期图的图像。一方面，我们以一种准确的方式表明，该地图的一部分参数化了非AdjaCent-Pure Hodge结构的扩展数据是Quasi-Affine。另一方面，相邻重量纯极化霍奇结构的扩展是由配备有天然theta束的紧凑型复合物（中间Jacobian）参数化的，在Griffiths横向方向上足质充足。 我们的证明是大量使用O最小性的，并且与B. Klingler的最新工作相关联，将$ \ mathbb {r} _ {an，exp} $ - 混合时期域和可允许的混合周期地图的可定义结构。
We prove a mixed version of a conjecture of Griffiths: that the closure of the image of any admissible mixed period map is quasiprojective, with a natural ample bundle. Specifically, we consider the map from the image of the mixed period map to the image of the period map of the associated graded. On the one hand, we show in a precise manner that the parts of this map parametrizing extension data of non-adjacent-weight pure Hodge structures are quasi-affine. On the other hand, extensions of adjacent-weight pure polarized Hodge structures are parametrized by a compact complex torus (the intermediate Jacobian) equipped with a natural theta bundle which is ample in Griffiths transverse directions. Our proof makes heavy use of o-minimality, and recent work with B. Klingler associating a $\mathbb{R}_{an,exp}$-definable structure to mixed period domains and admissible mixed period maps.
