Singularities of Fano varieties of lines on singular cubic fourfolds

Abstract

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 $K{3}^{[2]}$-type contraction and has a unique symplectic resolution.

v2: 14 pages, minor revision

References in corpus (2)

• The K3 category of a cubic fourfold
• Symplectic resolutions of the Hilbert squares of ADE surface singularities