On Varieties of Almost Minimal Degree Ii: a Rank-depth Formula
نویسندگان
چکیده
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.
منابع مشابه
On the arithmetical rank of a special class of minimal varieties
We study the arithmetical ranks and the cohomological dimensions of an infinite class of Cohen-Macaulay varieties of minimal degree. Among these we find, on the one hand, infinitely many set-theoretic complete intersections, on the other hand examples where the arithmetical rank is arbitrarily greater than the codimension.
متن کاملOn 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 P, whose ideal is generated in degree four. We also discuss the coordinate ring of secant varietie...
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 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 کاملSome remarks on inp-minimal and finite burden groups
We prove that any left-ordered inp-minimal group is abelian and we provide an example of a non-abelian left-ordered group of dp-rank 2. Furthermore, we establish a necessary condition for group to have finite burden involving normalizers of definable sets, reminiscent of other chain conditions for stable groups. 0 Introduction and preliminaries One of the model-theoretic properties that gained ...
متن کامل