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Session 2. Algebraic Geometry
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Twisted cubics on cubic fourfolds |
Manfred Lehn, Johannes Gutenberg--Universität, Mainz, Germany
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This is a report on joint work
with C. Lehn, C. Sorger, D. van Straten, and with N. Addington
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The moduli space of generalised twisted cubic curves on a smooth
cubic fourfold Y that does not contain a plane is shown to be
smooth, 10-dimensional and projective, and to admit a contraction to
an 8-dimensional smooth variety \(Z(Y)\) that is irreducible
holomorphic symplectic. Varying \(Z(Y)\) with \(Y\) gives a
complete 20-dimensional family of projective holomorphic symplectic
manifolds. If \(Y\) is a pfaffian cubic, \(Z(Y)\) is birational to
the fourth Hilbert scheme of points on the K3-surface associated to
Y by Beauville--Donagi.
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