On secant varieties of Compact Hermitian Symmetric Spaces

J. M. Landsberg; Jerzy Weyman

On secant varieties of Compact Hermitian Symmetric Spaces

Algebraic Geometry 2008-11-20 v2 Representation Theory

Authors: J. M. Landsberg , Jerzy Weyman

Abstract

We show that the secant varieties of rank three compact Hermitian symmetric spaces in their minimal homogeneous embeddings are normal, with rational singularities. We show that their ideals are generated in degree three - with one exception, the secant variety of the $21$ -dimensional spinor variety in $\pp{63}$ where we show the ideal is generated in degree four. We also discuss the coordinate rings of secant varieties of compact Hermitian symmetric spaces.

Keywords

secant varieties compact Hermitian symmetric spaces normal varieties rational singularities homogeneous embeddings spinor variety coordinate rings ideal generation

Cite

@article{arxiv.0802.3402,
  title  = {On secant varieties of Compact Hermitian Symmetric Spaces},
  author = {J. M. Landsberg and Jerzy Weyman},
  journal= {arXiv preprint arXiv:0802.3402},
  year   = {2008}
}

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15 pages, significantly cleaned up

On secant varieties of Compact Hermitian Symmetric Spaces

Abstract

Keywords

Cite

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