On secant varieties of Compact Hermitian Symmetric Spaces

2008/02/22 by J. M. Landsberg, Jerzy Weyman, Landsberg, J. M. +1
Mathematics · Medicine · #13P99 #14Q15 #15A69 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Phytoestrogen effects and research #Representation Theory (math.RT) #Tensor decomposition and applications #math.AG #math.RT #msc:13P99 #msc:14Q15 #msc:15A69

paper · pdf · doi:10.48550/arxiv.0802.3402

15 pages, significantly cleaned up

openalex publication_date 2008/02/22 · arxiv created 2008/11/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \pp63 where we show the ideal is generated in degree four. We also discuss the coordinate rings of secant varieties of compact Hermitian symmetric spaces.

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