On Secant Varieties of Compact Hermitian Symmetric Spaces
نویسنده
چکیده
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 P, whose ideal is generated in degree four. We also discuss the coordinate ring of secant varieties of compact Hermitian symmetric spaces.
منابع مشابه
Representation Theory and Projective Geometry
This article consists of three parts that are largely independent of one another. The first part deals with the projective geometry of homogeneous varieties, in particular their secant and tangential varieties. It culminates with an elementary construction of the compact Hermitian symmetric spaces and the closed orbits in the projectivization of the adjoint representation of a simple Lie algebr...
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