论文标题
通过Eckardt Cubic三倍的中间雅各布人的三次表面对的模量空间
The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds
论文作者
论文摘要
我们研究了由光滑的立方表面和光滑的超平面截面组成的模量空间，这是通过Laza，Pearlstein和第二名命名作者引起的Hodge理论周期图。建筑与这样一对所谓的Eckardt立方三倍相关，承认了这一差异，并且时期图将这一对二立方三分之一的中间Jacobian的抗不变性部分发送到了这一涉及的情况下。我们的主要结果是全球Torelli定理在此期间图中持有；即，周期图是配件的。为了证明结果，我们将中间雅各布的抗不变部分描述为各种分支盖的品种。我们的证明在相关的Prym地图上使用了Naranjo-Ortega，Bardelli-ciliberto-verra和Nagaraj-Ramanan的结果。实际上，我们能够通过描述正尺寸纤维来恢复这些prym地图之一的程度，并以同样的精神在Donagi-Smith的结果上，在Prym Map的程度上，用于连接的6曲线的典型双层覆盖物。
We study the moduli space of pairs consisting of a smooth cubic surface and a smooth hyperplane section, via a Hodge theoretic period map due to Laza, Pearlstein, and the second named author. The construction associates to such a pair a so-called Eckardt cubic threefold, admitting an involution, and the period map sends the pair to the anti-invariant part of the intermediate Jacobian of this cubic threefold, with respect to this involution. Our main result is that the global Torelli theorem holds for this period map; i.e., the period map is injective. To prove the result, we describe the anti-invariant part of the intermediate Jacobian as a Prym variety of a branched cover. Our proof uses results of Naranjo-Ortega, Bardelli-Ciliberto-Verra, and Nagaraj-Ramanan, on related Prym maps. In fact, we are able to recover the degree of one of these Prym maps by describing positive dimensional fibers, in the same spirit as a result of Donagi-Smith on the degree of the Prym map for connected étale double covers of genus 6 curves.
