Small schemes and varieties of minimal degree
نویسندگان
چکیده
منابع مشابه
Small Schemes and Varieties of Minimal
We prove that if X ⊂ Pr is any 2-regular scheme (in the sense of Castelnuovo-Mumford) then X is small. This means that if L is a linear space and Y := L ∩ X is finite, then Y is linearly independent in the sense that the dimension of the linear span of Y is deg Y − 1. The converse is true and well-known for finite schemes, but false in general. The main result of this paper is that the converse...
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 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 ...
متن کاملOrdinary abelian varieties having small embedding degree
Miyaji, Nakabayashi and Takano (MNT) gave families of group orders of ordinary elliptic curves with embedding degree suitable for pairing applications. In this paper we generalise their results by giving families corresponding to non-prime group orders. We also consider the case of ordinary abelian varieties of dimension 2. We give families of group orders with embedding degrees 5, 10 and 12.
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2006
ISSN: 1080-6377
DOI: 10.1353/ajm.2006.0043