Singularities of secant varieties

Chih-Chi Chou; Lei Song

Singularities of secant varieties

Algebraic Geometry 2017-02-02 v2

Authors: Chih-Chi Chou , Lei Song

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.

Keywords

projective varieties

Cite

@article{arxiv.1503.01099,
  title  = {Singularities of secant varieties},
  author = {Chih-Chi Chou and Lei Song},
  journal= {arXiv preprint arXiv:1503.01099},
  year   = {2017}
}

Comments

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

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