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• W3109189020 abstract "We show that the moduli space $overline{M}_X(v)$ of Gieseker stable sheaves on a smooth cubic threefold $X$ with Chern character $v = (3,-H,-H^2/2,H^3/6)$ is smooth and of dimension four. Moreover, the Abel-Jacobi map to the intermediate Jacobian of $X$ maps it birationally onto the theta divisor $Theta$, contracting only a copy of $X subset overline{M}_X(v)$ to the singular point $0 in Theta$. We use this result to give a new proof of a categorical version of the Torelli theorem for cubic threefolds, which says that $X$ can be recovered from its Kuznetsov component $operatorname{Ku}(X) subset mathrm{D}^{mathrm{b}}(X)$. Similarly, this leads to a new proof of the description of the singularity of the theta divisor, and thus of the classical Torelli theorem for cubic threefolds, i.e., that $X$ can be recovered from its intermediate Jacobian." @default.
• W3109189020 created "2020-12-07" @default.
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• W3109189020 date "2020-11-24" @default.
• W3109189020 modified "2023-09-26" @default.
• W3109189020 title "The desingularization of the theta divisor of a cubic threefold as a moduli space" @default.
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