Singularities of secant varieties

Abstract

We study the singularities of the secant variety $\Sigma (X,L)$ associated to a smooth variety $X$ embedded by a sufficiently positive adjoint bundle $L$. We show that $\Sigma (X,L)$ is always Du Bois singular. Examples of secant varieties with worse singularities when $L$ has weak positivity are provided. We also give a necessary and sufficient condition for $\Sigma (X,L)$ to have rational singularities.

Under a referee's request, non Du Bois secant varieties are presented in Section 4

References in corpus (2)

• Singularities with respect to Mather-Jacobian discrepancies
• The Kodaira dimension of spaces of rational curves on low degree hypersurfaces

Cited by in corpus (1)

• On direct images of twisted pluricanonical sheaves on normal varieties