Twisted cubics on cubic fourfolds

By C. Lehn, M. Lehn, Christoph Sorger, Duco van Straten. 2013

114 citations recorded by the source corpus.

We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space M_3(Y) of twisted cubics on a smooth cubic fourfold Y that does not contain a plane is shown to be smooth and to admit a contraction M_3(Y) -> Z(Y) to a projective eight-dimensional symplectic manifold Z(Y). The construction is based on results on linear determinantal representations of singular cubic surfaces.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/13f77356930c8e40f10a18dd2f9c3891082653f5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. P. Stellari
2. Emanuele Macrì
3. D. Huybrechts
4. Claire Voisin
5. R. Laza
6. Giulia Saccà
7. J. Kollár
8. Alexander Perry

In Mathematical Physics

1. P. Stellari
2. Emanuele Macrì
3. D. Huybrechts
4. Giulia Saccà
5. Claire Voisin
6. J. Kollár
7. R. Laza
8. Arend Bayer

Citations in the corpus

• Remarks on degenerations of hyper-K\"ahler manifolds (2017, methodology): “The LLSvS eightfolds were constructed in [LLSvS13], and were proved in [AL14] (see also [Leh15]) to be deformation equivalent to S([4]).”
• Remarks And Questions On Coisotropic Subvarieties and 0-Cycles of Hyper-Kähler Varieties (2015, methodology): “onstructions and various evidences for these conjectures, in three cases: Hilbert schemes of K3 surfaces, Fano varieties of lines of cubic fourfolds, and finally the more recent 8-folds constructed in [17] starting from the Hilbert scheme of cubic rational curves on cubic fourfolds. Thanks. I thank F”
• Hodge theory and derived categories of cubic fourfolds (2012, unknown): “ects on S t. Projecting O x;x2X t, into A Xt gives an object P xwhich sits inside an 8-dimensional holomorphic symplectic moduli space M tof objects of A Xt ˆD(X t), as studied in the recent preprint [29]. Using the equivalence twe can also consider M tto be a moduli space of objects on the K3 surfa”
• Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces (2018, methodology): “ hyperka¨hler manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface (see [BD85]). More recently, it was proved by Christian Lehn, Manfred Lehn, Sorger and van Straten [LLSvS17] that the moduli space of generalized twisted cubics inside a cubic fourfold also gives ris”