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

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Arend Bayer
  • Sjoerd Beentjes
  • Soheyla Feyzbakhsh
  • Georg Hein
  • Benjamin Schmidt

Research Organisations

External Research Organisations

  • University of Edinburgh
  • Imperial College London
  • University of Duisburg-Essen
  • University of Amsterdam

Details

Original languageEnglish
Pages (from-to)127–160
Number of pages34
JournalGeometry and Topology
Volume28
Issue number1
Publication statusPublished - 27 Feb 2024

Abstract

We show that the moduli space M¯¯¯¯¯X(v) of Gieseker stable sheaves on a smooth cubic threefold X with Chern character v=(3,−H,−H2/2,H3/6) is smooth and of dimension four. Moreover, the Abel-Jacobi map to the intermediate Jacobian of X maps it birationally onto the theta divisor Θ, contracting only a copy of X⊂M¯¯¯¯¯X(v) to the singular point 0∈Θ.
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 Ku(X)⊂Db(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.

Keywords

    cubic threefolds, derived categories, stability conditions

ASJC Scopus subject areas

Cite this

The desingularization of the theta divisor of a cubic threefold as a moduli space. / Bayer, Arend; Beentjes, Sjoerd; Feyzbakhsh, Soheyla et al.
In: Geometry and Topology, Vol. 28, No. 1, 27.02.2024, p. 127–160.

Research output: Contribution to journal › Article › Research › peer review

Bayer, A, Beentjes, S, Feyzbakhsh, S, Hein, G, Martinelli, D, Rezaee, F & Schmidt, B 2024, 'The desingularization of the theta divisor of a cubic threefold as a moduli space', Geometry and Topology, vol. 28, no. 1, pp. 127–160. https://doi.org/10.2140/gt.2024.28.127
Bayer, A., Beentjes, S., Feyzbakhsh, S., Hein, G., Martinelli, D., Rezaee, F., & Schmidt, B. (2024). The desingularization of the theta divisor of a cubic threefold as a moduli space. Geometry and Topology, 28(1), 127–160. https://doi.org/10.2140/gt.2024.28.127
Bayer A, Beentjes S, Feyzbakhsh S, Hein G, Martinelli D, Rezaee F et al. The desingularization of the theta divisor of a cubic threefold as a moduli space. Geometry and Topology. 2024 Feb 27;28(1):127–160. doi: 10.2140/gt.2024.28.127
Bayer, Arend ; Beentjes, Sjoerd ; Feyzbakhsh, Soheyla et al. / The desingularization of the theta divisor of a cubic threefold as a moduli space. In: Geometry and Topology. 2024 ; Vol. 28, No. 1. pp. 127–160.
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AU - Beentjes, Sjoerd

AU - Feyzbakhsh, Soheyla

AU - Hein, Georg

AU - Martinelli, Diletta

AU - Rezaee, Fatemeh

AU - Schmidt, Benjamin

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