On secant varieties of Compact Hermitian Symmetric Spaces

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.Comment: 15 pages, significantly cleaned u

On the minimal free resolution of the universal ring for resolutions of length two

AbstractHochster established the existence of a commutative noetherian ring C˜ and a universal resolution U of the form 0→C˜e→C˜f→C˜g→0 such that for any commutative noetherian ring S and any resolution V equal to 0→Se→Sf→Sg→0, there exists a unique ring homomorphism C˜→S with V=U⊗C˜S. In the present paper we assume that f=e+g and we find the minimal resolution of C˜⊗ZQ by free B-modules, where B is a polynomial ring over the field of rational numbers. The modules of the resolution are described in terms of Schur functors. The graded strands of the differential are described in terms of Pieri maps