The Defect of a Cubic Threefold and Applications to Intermediate Jacobian Fibrations

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A cubic threefold's defect indicates it is not Q-factorial if it includes a plane or cubic scroll, and this leads to strong geometric implications.
The defect calculated is related to topological data concerning a curve of lines passing through singular points, illuminating singularities' impact on structure.
The Hodge structure on the middle cohomology is expressed in terms of both the defect and local singularity invariants, highlighting intricate relationships.
This work connects the defect to the existence of compactified intermediate Jacobian fibrations with irreducible fibers linked to cubic fourfolds.

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Analysis reveals defect as a measure of Q-factoriality in cubic threefolds, implying connections to intermediate Jacobian fibrations.

Marquand et al. (2025) studied this question.

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