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Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations
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Li, Chunyi, Pertusi, Laura and Zhao, Xiaolei (2022) Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations. Advances in Mathematics, 408 (Part A). 108584. doi:10.1016/j.aim.2022.108584 ISSN 0001-8708.
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WRAP-Elliptic-quintics-cubic-fourfolds-o-grady-10-lagrangian-fibrations-2022.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (720Kb) | Preview |
Official URL: https://doi.org/10.1016/j.aim.2022.108584
Abstract
For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai vector in the Kuznetsov component of Y. We show that with a certain choice of stability conditions, M admits a symplectic resolution , which is a smooth projective hyperkähler manifold, deformation equivalent to the 10-dimensional examples constructed by O'Grady. As applications, we show that a birational model of provides a hyperkähler compactification of the twisted family of intermediate Jacobians associated to Y. This generalizes the previous result of Voisin [58] in the very general case. We also prove that is the MRC quotient of the main component of the Hilbert scheme of quintic elliptic curves in Y, confirming a conjecture of Castravet.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| SWORD Depositor: | Library Publications Router | ||||||||
| Library of Congress Subject Headings (LCSH): | Surfaces, Algebraic, Enriques surfaces , Calabi-Yau manifolds , Algebraic varieties, Derived categories (Mathematics) | ||||||||
| Journal or Publication Title: | Advances in Mathematics | ||||||||
| Publisher: | Academic Press | ||||||||
| ISSN: | 0001-8708 | ||||||||
| Official Date: | 28 October 2022 | ||||||||
| Dates: |
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| Volume: | 408 | ||||||||
| Number: | Part A | ||||||||
| Article Number: | 108584 | ||||||||
| DOI: | 10.1016/j.aim.2022.108584 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 29 July 2022 | ||||||||
| Date of first compliant Open Access: | 25 July 2023 |
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