For a variety X of dimension n in P^r, r> n(k+1)+k-1, the k-th secant order of X is the number m_k(X) of (k+1)-secant k-spaces passing through a general point of the k-th secant variety. We show that, if r>n(k+1)+k, then m_k(X)=1 unless X is k--weakly defective. Furthermore we give a complete classification of surfaces X in P^r, r>3k+2, for which m_k(X)>1
Abstract. Fix Integers n> 0, k> 0. Here we prove the existence on an integer d(n, k) with the ...
Let Vt=P1x \u2026 x P1 be the product of t copies of the 1-dimensional projective space P1, embedded...
A projective variety X is ‘k-weakly defective’ when its intersection with a general (k + 1)-tangent ...
For a variety X of dimension n in P^r, r> n(k+1)+k-1, the k-th secant order of X is the number m_k(X...
Given a closed subvariety X in a projective space, the rank with respect to X of a point p in this p...
Let Vn be the Segre embedding of P1 x ... x P1 (n times). We prove that the higher secant varieties ...
Let X(1,d) denote the Segre-Veronese embedding of Pn x Pm via the sections of the sheaf O(1, d). We ...
Given a variety X embedded in a projective space PV , the (k - 1)-st secant variety of X, denoted kX...
We classify all smooth threefolds X in P^N , for which the Grassmann secant variety G(1;2) (i.e. the...
Let $X^{(n,m)}_{(1,d)}$ denote the Segre-Veronese embedding of $\mathbb{P}^n \times \mathbb{P}^m$ vi...
Let G(k,n) be the Grassmannian of k-subspaces in an n- dimensional complex vector space, k ≥ 3. Give...
We generalize Zak's theorems on tangencies and on linear normality as well as Zak's definition and c...
Let V n V_n be the Segre embedding of ...
Abstract. This paper studies the dimension of secant varieties to Segre va-rieties. The problem is c...
We give the full classification of irreducible projective threefolds whose k-secant variety has dim...
Abstract. Fix Integers n> 0, k> 0. Here we prove the existence on an integer d(n, k) with the ...
Let Vt=P1x \u2026 x P1 be the product of t copies of the 1-dimensional projective space P1, embedded...
A projective variety X is ‘k-weakly defective’ when its intersection with a general (k + 1)-tangent ...
For a variety X of dimension n in P^r, r> n(k+1)+k-1, the k-th secant order of X is the number m_k(X...
Given a closed subvariety X in a projective space, the rank with respect to X of a point p in this p...
Let Vn be the Segre embedding of P1 x ... x P1 (n times). We prove that the higher secant varieties ...
Let X(1,d) denote the Segre-Veronese embedding of Pn x Pm via the sections of the sheaf O(1, d). We ...
Given a variety X embedded in a projective space PV , the (k - 1)-st secant variety of X, denoted kX...
We classify all smooth threefolds X in P^N , for which the Grassmann secant variety G(1;2) (i.e. the...
Let $X^{(n,m)}_{(1,d)}$ denote the Segre-Veronese embedding of $\mathbb{P}^n \times \mathbb{P}^m$ vi...
Let G(k,n) be the Grassmannian of k-subspaces in an n- dimensional complex vector space, k ≥ 3. Give...
We generalize Zak's theorems on tangencies and on linear normality as well as Zak's definition and c...
Let V n V_n be the Segre embedding of ...
Abstract. This paper studies the dimension of secant varieties to Segre va-rieties. The problem is c...
We give the full classification of irreducible projective threefolds whose k-secant variety has dim...
Abstract. Fix Integers n> 0, k> 0. Here we prove the existence on an integer d(n, k) with the ...
Let Vt=P1x \u2026 x P1 be the product of t copies of the 1-dimensional projective space P1, embedded...
A projective variety X is ‘k-weakly defective’ when its intersection with a general (k + 1)-tangent ...
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