Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 57, Number 4 (2017), 789-806.
On the geometry of the Lehn–Lehn–Sorger–van Straten eightfold
In this article we make a few remarks about the geometry of the holomorphic symplectic manifold constructed by Lehn, Lehn, Sorger, and van Straten as a two-step contraction of the variety of twisted cubic curves on a cubic fourfold . We show that is birational to a component of the moduli space of stable sheaves in the Calabi–Yau subcategory of the derived category of . Using this description we deduce that the twisted cubics contained in a hyperplane section of give rise to a Lagrangian subvariety . For a generic choice of the hyperplane, is birational to the theta-divisor in the intermediate Jacobian .
Kyoto J. Math., Volume 57, Number 4 (2017), 789-806.
Received: 5 April 2016
Accepted: 10 June 2016
First available in Project Euclid: 9 June 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry
Shinder, Evgeny; Soldatenkov, Andrey. On the geometry of the Lehn–Lehn–Sorger–van Straten eightfold. Kyoto J. Math. 57 (2017), no. 4, 789--806. doi:10.1215/21562261-2017-0014. https://projecteuclid.org/euclid.kjm/1496973624