Singularities of Fano varieties of lines on singular cubic fourfolds

31 Mar 2018  ·  Yamagishi Ryo ·

Let $X$ be a cubic fourfold that has only simple singularities and does not contain a plane. We prove that the Fano variety of lines on $X$ has the same analytic type of singularity as the Hilbert scheme of two points on a surface with only ADE-singularities... This is shown as a corollary to the characterization of a singularity that is obtained as a $K3^{[2]}$-type contraction and has a unique symplectic resolution. read more

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Algebraic Geometry