For a smooth cubic fourfold Y , we study the moduli space M of semistable objects of Mukai vector 2λ1 + 2λ2 in the Kuznetsov component of Y . We show that with a certain choice of stability conditions, M admits a symplectic resolution ̃M , which is a smooth projective hyperk ̈ahler manifold, deformation equivalent to the 10-dimensional ex- amples constructed by O’Grady. As applications, we show that a birational model of ̃M provides a hyperk ̈ahler compactification of the twisted family of intermediate Jacobians as- sociated to Y . This generalizes the previous result of Voisin [Voi18] in the very general case. We also prove that ̃M is the MRC quotient of the main component of the Hilbert scheme of quintic elliptic curves in Y , confirming a conjecture of Castravet.

Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations / C. Li, L. Pertusi, X. Zhao. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 408:(2022), pp. 108584.1-108584.44. [Epub ahead of print] [10.1016/j.aim.2022.108584]

Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations

L. Pertusi;
2022

Abstract

For a smooth cubic fourfold Y , we study the moduli space M of semistable objects of Mukai vector 2λ1 + 2λ2 in the Kuznetsov component of Y . We show that with a certain choice of stability conditions, M admits a symplectic resolution ̃M , which is a smooth projective hyperk ̈ahler manifold, deformation equivalent to the 10-dimensional ex- amples constructed by O’Grady. As applications, we show that a birational model of ̃M provides a hyperk ̈ahler compactification of the twisted family of intermediate Jacobians as- sociated to Y . This generalizes the previous result of Voisin [Voi18] in the very general case. We also prove that ̃M is the MRC quotient of the main component of the Hilbert scheme of quintic elliptic curves in Y , confirming a conjecture of Castravet.
Cubic fourfolds; Stability conditions; Intermediate Jacobian
Settore MAT/03 - Geometria
Article (author)
File in questo prodotto:
File Dimensione Formato  
Elliptic_quintics (1).pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 615.62 kB
Formato Adobe PDF
615.62 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/940126
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? ND
social impact