论文标题
通过中级雅各布人的非ckardt类型相互作用的立方三倍的模量空间
The moduli space of cubic threefolds with a non-Eckardt type involution via intermediate Jacobians
论文作者
论文摘要
立方三倍有两种类型：Eckardt类型（已由第一个命名和第三个命名作者研究）和非Ceckardt类型。在这里，我们研究了具有非ceck型相关性的立方三倍，其固定基因座由一条线和立方曲线组成。具体而言，我们考虑的时期图将与中间Jacobian不变部分的非ckardt类型相互作用发送的三次三倍。主要的结果是全球Torelli定理在周期图中持有。为了证明定理，我们将立方三倍从点式固定线投射出三倍，并展示中间雅各布的不变部分，作为稳定曲线的（伪）双盖的prym品种。证明依赖于Ikeda和Naranjo-Ortega对相关PRYM映射的注射率的结果。我们还通过一般不变线的投影描述了中间雅各布的不变部分，并表明这两个描述与Bigonal结构相关。
There are two types of involutions on a cubic threefold: the Eckardt type (which has been studied by the first named and the third named authors) and the non-Eckardt type. Here we study cubic threefolds with a non-Eckardt type involution, whose fixed locus consists of a line and a cubic curve. Specifically, we consider the period map sending a cubic threefold with a non-Eckardt type involution to the invariant part of the intermediate Jacobian. The main result is that the global Torelli Theorem holds for the period map. To prove the theorem, we project the cubic threefold from the pointwise fixed line and exhibit the invariant part of the intermediate Jacobian as a Prym variety of a (pseudo-)double cover of stable curves. The proof relies on a result of Ikeda and Naranjo-Ortega on the injectivity of the related Prym map. We also describe the invariant part of the intermediate Jacobian via the projection from a general invariant line and show that the two descriptions are related by the bigonal construction.
