The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds, not even as a map to the Satake compactification of the moduli space of principally polarized abelian fivefolds. A much better "wonderful" compactification of the space of cubic threefolds was constructed by the first and fourth authors --- it has a modular interpretation, and divisorial normal crossing boundary. We prove that the intermediate Jacobian map extends to a morphism from the wonderful compactification to the second Voronoi toroidal compactification of the moduli of principally polarized abelian fivefolds --- the first and fourth author previously showed that it extends to the Satake compactification. Since the second Voronoi compactification has a modular interpretation, our extended intermediate Jacobian map encodes all of the geometric information about the degenerations of intermediate Jacobians, and allows for the study of the geometry of cubic threefolds via degeneration techniques. As one application we give a complete classification of all degenerations of intermediate Jacobians of cubic threefolds of torus rank 1 and 2.

中文翻译：

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三次三重模及其中间雅可比方程的完全模

中间雅可比图谱与其平滑的三次雅可比谱图相关联，而中间雅可比谱图未扩展到三次三倍谱图空间的GIT紧致化，甚至未映射到主要极化的阿贝尔倍数的模空间的Satake压缩。第一和第四作者构造了三次三倍空间的更好的“奇妙”压实-它具有模块化解释和除数法线交叉边界。我们证明中间雅可比图谱从奇化压实扩展到第二次Voronoi环面压实，主要是极化的阿贝尔倍数模量的第二次Voronoi环面压实---第一和第四作者先前表明它扩展到了Satake压实。由于第二次Voronoi压缩具有模块化解释，因此我们扩展的中间雅可比图谱对有关中间雅可比派生式的所有几何信息进行编码，并允许通过退化技术研究立方三倍体的几何形状。作为一种应用，我们给出了圆环等级为1和2的立方三倍三次的中间Jacobian的所有简并的完整分类。