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Twisted cubics on cubic fourfolds

Christian Lehn, Manfred Lehn, Christoph Sorger, Duco van Straten

Number 28
Authors Christian Lehn
Duco van Straten
Christoph Sorger
Manfred Lehn
Year 2013

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.

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