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Abstract des Vortrages von Christian Lehn

Rational curves on singular cubic fourfolds

We study moduli spaces of rational curves on singular cubic hypersurfaces of dimension 4. In degree three they admit a contraction to a singular symplectic variety. These symplectic varieties carry (rational) Lagrangian fibrations by work of Starr. Using Namikawa's theory on deformations and crepant resolutions of singular symplectic varieties, we show that the symplectic eighfolds constructed in a preceding joint work with Lehn, Sorger and van Straten are deformations of Hilbert schemes of 4 points on a K3 surface.