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The aim is to characterize the intermediate Jacobian of smooth cubic threefolds and identify its properties within the moduli space.

July 26, 2026Open Access

Cubic Threefold Jacobians: A Special Subvariety of \(A_5\) — E8 Intelligence Research

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The aim is to characterize the intermediate Jacobian of smooth cubic threefolds and identify its properties within the moduli space.
Examination of the intermediate Jacobian for a smooth cubic threefold in projective space.
Analysis of the period map from cubic threefolds to the moduli space of principally polarized abelian varieties.
Investigation of the monodromy group for cubic threefold families.
The intermediate Jacobian is a 5-dimensional principally polarized abelian variety with a singular odd 2-torsion point on its theta divisor.
The moduli locus of these Jacobians is a special subvariety of the moduli space A5.
Closure in the Satake compactification reveals connections to degenerations with nodes.

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Demonstrates a special geometric structure in cubic threefolds, suggesting new insights into moduli space characteristics.

Andrew Stewart Caldin (2026) studied this question.

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