Singularities of secant varieties

Chih-Chi Chou, Lei Song

Published 2015-03-03Version 1

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. We also give a necessary and sufficient condition for $\Sigma(X, L)$ to have rational singularities.