指标2的Fano三倍的Kuznetsov分量上的模空间

Pub Date : 2019-08-28 DOI:10.46298/epiga.2022.7047

Matteo Altavilla, Marina Petković, Franco Rota

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引用次数: 20

摘要

索引2和Picardrank 1的Fano三重$Y$的一般超平面截面是del Pezzo曲面，并且它们的Picard群与根系统有关。对于相应的根，我们将$Y$的库兹涅佐夫分量中的对象关联起来，并使用Bayer、Lahoz、Macr\`i和Stellari构造的稳定条件和Abel-Jacobi映射来研究它们的模空间。我们确定了模空间的同构于$Y$本身的一个子变种，并且作为一个应用，我们证明了一般四次二重固体的（精化的）范畴Torelli定理。

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Moduli spaces on the Kuznetsov component of Fano threefolds of index 2

General hyperplane sections of a Fano threefold $Y$ of index 2 and Picard rank 1 are del Pezzo surfaces, and their Picard group is related to a root system. To the corresponding roots, we associate objects in the Kuznetsov component of $Y$ and investigate their moduli spaces, using the stability condition constructed by Bayer, Lahoz, Macr\`i, and Stellari, and the Abel--Jacobi map. We identify a subvariety of the moduli space isomorphic to $Y$ itself, and as an application we prove a (refined) categorical Torelli theorem for general quartic double solids.

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