Twisted cubics on cubic fourfolds

2013/05/01 by Lehn, Christian, Lehn, Manfred, Sorger, Christoph +1 · 3 citations
#14C21 #14J10 #14J35 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14C05 #Secondary 14J26

paper · doi:10.48550/arxiv.1305.0178

Abstract

We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space M₃(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 M₃(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.

Cited by

• Projective models for Hilbert squares of K3 surfaces
• Peskine sixfolds and Debarre-Voisin fourfolds with associated cubic fourfolds
• Galois covers of Calabi-Yau manifolds

Related

• Twisted cubics on singular cubic fourfolds - On Starr's fibration
• Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects
• Lagrangian embeddings of cubic fourfolds containing a plane
• Twisted cubics on cubic fourfolds and stability conditions
• Moduli spaces of twisted K3 surfaces and cubic fourfolds