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The research aims to investigate the properties of a moduli space of Gieseker stable sheaves on cubic threefolds.

February 19, 2026Open Access

The desingularization of the theta divisor of a cubic threefold as a moduli space

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The research aims to investigate the properties of a moduli space of Gieseker stable sheaves on cubic threefolds.
Analyze the moduli space of Gieseker stable sheaves with specific Chern characters.
Examine the birational relationship between the moduli space and the theta divisor through the Abel-Jacobi map.
Provide proofs linking results to the Torelli theorem for cubic threefolds.
The moduli space is found to be smooth and has a dimension of four.
The Abel-Jacobi map birationally maps the moduli space onto the theta divisor, contracting a copy of the cubic threefold to a point.
New proofs of both categorical and classical versions of the Torelli theorem for cubic threefolds are established.

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The work demonstrates a smooth moduli space of stable sheaves, revealing connections to classical theorems.

Bayer et al. (2024) studied this question.

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