三次三叠模空间的第二种基本形式

Pub Date : 2023-10-27 DOI:10.46298/epiga.2023.9962

Elisabetta Colombo, Paola Frediani, Juan Carlos Naranjo, Gian Pietro Pirola

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摘要

本文研究了在三次矩阵的中间雅可比矩阵轨迹下的西格尔度规的第二种基本形式。我们证明了这第二种基本形式的非平凡象包含在一个合适的乘法映射的核中。一些成分是:三次三重的圆锥束结构，Prym理论，高斯映射和雅可比理想。

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The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$

We study the second fundamental form of the Siegel metric in $\mathcal A_5$ restricted to the locus of intermediate Jacobians of cubic threefolds. We prove that the image of this second fundamental form, which is known to be non-trivial, is contained in the kernel of a suitable multiplication map. Some ingredients are: the conic bundle structure of cubic threefolds, Prym theory, Gaussian maps and Jacobian ideals.

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