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arXiv · 1305.0178

Twisted cubics on cubic fourfolds

Christian Lehn·Manfred Lehn·Christoph Sorger·Duco van Straten
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Abstract

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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Christian Lehn, Manfred Lehn, Christoph Sorger, Duco van Straten. 2013-07-19. Twisted cubics on cubic fourfolds. https://arxiv.org/abs/1305.0178

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