Data di Pubblicazione:
2022
Citazione:
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]
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Cubic fourfolds; Stability conditions; Intermediate Jacobian
Elenco autori:
C. Li, L. Pertusi, X. Zhao
Link alla scheda completa: