Gushel—Mukai变种:中间雅可比矩阵

Pub Date : 2020-02-13 DOI:10.46298/epiga.2020.volume4.6475

O. Debarre, A. Kuznetsov

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引用次数: 17

摘要

我们描述了3维或5维的Gushel-Mukai变量$X$的中间雅可比矩阵:如果$A$是与$X$相关的拉格朗日空间，我们证明了$X$的中间雅可比矩阵同构于与$A$相关的两个对偶eisenbud - popescu - walter曲面的任意一个正则双覆盖的Albanese变体。作为应用，我们描述了Gushel-Mukai三倍和五倍的周期图。评论:48页。我们关于Gushel-Mukai品种几何的系列文章的最新补充;V2:小的风格改进，结果不变;V3:小改进;v4:最终版本，以EPIGA发布

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Gushel--Mukai varieties: intermediate Jacobians

We describe intermediate Jacobians of Gushel-Mukai varieties $X$ of dimensions 3 or 5: if $A$ is the Lagrangian space associated with $X$, we prove that the intermediate Jacobian of $X$ is isomorphic to the Albanese variety of the canonical double covering of any of the two dual Eisenbud-Popescu-Walter surfaces associated with $A$. As an application, we describe the period maps for Gushel-Mukai threefolds and fivefolds. Comment: 48 pages. Latest addition to our series of articles on the geometry of Gushel-Mukai varieties; v2: minor stylistic improvements, results unchanged; v3: minor improvements; v4: final version, published in EPIGA

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