Results 1 
5 of
5
On tangential varieties of rational homogeneous varieties
 Jour. Lond. Math. Soc
"... Abstract. We determine which tangential varieties of homogeneously embedded rational homogeneous varieties are spherical. We determine the homogeneous coordinate rings and rings of covariants of the tangential varieties of homogenously embedded compact Hermitian symmetric spaces (CHSS). We give boun ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract. We determine which tangential varieties of homogeneously embedded rational homogeneous varieties are spherical. We determine the homogeneous coordinate rings and rings of covariants of the tangential varieties of homogenously embedded compact Hermitian symmetric spaces (CHSS). We give bounds on the degrees of generators of the ideals of tangential varieties of CHSS and obtain more explicit infomation about the ideals in certain cases. 1.
NONDEFECTIVITY OF GRASSMANNIANS OF PLANES
, 901
"... Abstract. Let Gr(k, n) be the Plücker embedding of the Grassmann variety of projective kplanes in P n. For a projective variety X, let σs(X) denote the variety of its s − 1 secant planes. More precisely, σs(X) denotes the Zariski closure of the union of linear spans of stuples of points lying on X ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract. Let Gr(k, n) be the Plücker embedding of the Grassmann variety of projective kplanes in P n. For a projective variety X, let σs(X) denote the variety of its s − 1 secant planes. More precisely, σs(X) denotes the Zariski closure of the union of linear spans of stuples of points lying on X. We exhibit two functions s0(n) ≤ s1(n) such that σs(Gr(2, n)) has the expected dimension whenever n ≥ 9 and either s ≤ s0(n) or s1(n) ≤ s. Both s0(n) and s1(n) are asymptotic to n2. This yields, asymptotically, the typical rank of 18 an element of ∧3 Cn+1. Finally, we classify all defective σs(Gr(k, n)) for s ≤ 6 and provide geometric arguments underlying each defective case. 1.
On Spinor Varieties and Their Secants
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2009
"... We study the secant variety of the spinor variety, focusing on its equations of degree three and four. We show that in type Dn, cubic equations exist if and only if n ≥ 9. In general the ideal has generators in degrees at least three and four. Finally we observe that the other Freudenthal varieties ..."
Abstract
 Add to MetaCart
We study the secant variety of the spinor variety, focusing on its equations of degree three and four. We show that in type Dn, cubic equations exist if and only if n ≥ 9. In general the ideal has generators in degrees at least three and four. Finally we observe that the other Freudenthal varieties exhibit strikingly similar behaviors.
Symmetry, Integrability and Geometry: Methods and Applications On Spinor Varieties and Their Secants ⋆
, 904
"... doi:10.3842/SIGMA.2009.078 ..."