Complete moduli of cubic threefolds and their intermediate Jacobians

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Sebastian Casalaina-Martin
  • Samuel Grushevsky
  • Klaus Hulek
  • Radu Laza

Externe Organisationen

  • University of Colorado Boulder
  • Stony Brook University (SBU)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)259-316
Seitenumfang58
FachzeitschriftProceedings of the London Mathematical Society
Jahrgang122
Ausgabenummer2
Frühes Online-Datum17 Aug. 2020
PublikationsstatusVeröffentlicht - 1 Feb. 2021

Abstract

The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds, not even as a map to the Satake compactification of the moduli space of principally polarized abelian fivefolds. A better ‘wonderful’ compactification (Formula presented.) of the space of cubic threefolds was constructed by the first and fourth authors — it has a modular interpretation, and divisorial normal crossing boundary. We prove that the intermediate Jacobian map extends to a morphism from (Formula presented.) to the second Voronoi toroidal compactification of (Formula presented.) — the first and fourth author previously showed that it extends to the Satake compactification. Since the second Voronoi compactification has a modular interpretation, our extended intermediate Jacobian map encodes all of the geometric information about the degenerations of intermediate Jacobians, and allows for the study of the geometry of cubic threefolds via degeneration techniques. As one application, we give a complete classification of all degenerations of intermediate Jacobians of cubic threefolds of torus rank 1 and 2.

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Complete moduli of cubic threefolds and their intermediate Jacobians. / Casalaina-Martin, Sebastian; Grushevsky, Samuel; Hulek, Klaus et al.
in: Proceedings of the London Mathematical Society, Jahrgang 122, Nr. 2, 01.02.2021, S. 259-316.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Casalaina-Martin S, Grushevsky S, Hulek K, Laza R. Complete moduli of cubic threefolds and their intermediate Jacobians. Proceedings of the London Mathematical Society. 2021 Feb 1;122(2):259-316. Epub 2020 Aug 17. doi: 10.1112/plms.12375
Casalaina-Martin, Sebastian ; Grushevsky, Samuel ; Hulek, Klaus et al. / Complete moduli of cubic threefolds and their intermediate Jacobians. in: Proceedings of the London Mathematical Society. 2021 ; Jahrgang 122, Nr. 2. S. 259-316.
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N1 - Funding Information: Research of the first author was supported in part by NSF grant DMS‐11‐01333 and a Simons Foundation Collaboration Grant for Mathematicians (317572). Research of the second author was supported in part by NSF grants DMS‐12‐01369 and DMS‐15‐01265, and a Simons Fellowship in mathematics. Research of the third author was supported in part by DFG grant Hu‐337/6‐2. Research of the fourth author was supported in part by NSF grants DMS‐12‐00875 and DMS‐12‐54812.

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