منابع مشابه
On Varieties of Almost Minimal Degree I : Secant Loci of Rational Normal Scrolls
To provide a geometrical description of the classification theory and the structure theory of varieties of almost minimal degree, that is of non-degenerate irreducible projective varieties whose degree exceeds the codimension by precisely 2, a natural approach is to investigate simple projections of varieties of minimal degree. Let X̃ ⊂ P K be a variety of minimal degree and of codimension at le...
متن کاملOn Varieties of Almost Minimal Degree Ii: a Rank-depth Formula
We show that the arithmetic depth of the projection Xp of a rational normal scroll X̃ ⊂ P K from a point p ∈ P K \X̃ can be expressed in terms of the rank of the matrix M ′(p), where M ′ is the matrix of linear forms whose 3× 3 minors define the secant variety of X̃.
متن کاملGerms of Integrable Forms and Varieties of Minimal Degree
We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω(C, 0). We prove that the irreducible components with dimension comparable with the rank of W are of minimal degree.
متن کاملOn the Universal Gröbner Bases of Varieties of Minimal Degree
A universal Gröbner basis of an ideal is the union of all its reduced Gröbner bases. It is contained in the Graver basis, the set of all primitive elements. Obtaining an explicit description of either of these sets, or even a sharp degree bound for their elements, is a nontrivial task. In their ’95 paper, Graham, Diaconis and Sturmfels give a nice combinatorial description of the Graver basis f...
متن کاملSums of Squares and Varieties of Minimal Degree
The study of nonnegativity and its relation with sums of squares is a basic challenge in real algebraic geometry. The classification of varieties of minimal degree is one of the milestones of classical complex algebraic geometry. The goal of this paper is to establish the deep connection between these apparently separate topics. To achieve this, let X ⊆ P be an embedded real projective variety ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.02.027