منابع مشابه
Separators of Points in a Multiprojective Space
In this note we develop some of the properties of separators of points in a multiprojective space. In particular, we prove multigraded analogs of results of Geramita, Maroscia, and Roberts relating the Hilbert function of X and X \ {P} via the degree of a separator, and Abrescia, Bazzotti, and Marino relating the degree of a separator to shifts in the minimal multigraded free resolution of the ...
متن کاملSeparators of Fat Points in Multiprojective Spaces
Let Z be a set of fat points in a multiprojective space Pn × · · · × Pn . We introduce definitions for the separator of a fat point and the degree of a fat point in this context, and we study some of their properties. Our definition has been picked so that when we specialize to the cases: (a) Z is a reduced set of points in Pn , (b) Z is a set of fat points in Pn, or (c) Z is a reduced set of p...
متن کاملAlgebraic curves, rich points, and doubly-ruled surfaces
We study the structure of collections of algebraic curves in three dimensions that have many curve-curve incidences. In particular, let k be a field and let L be a collection of n space curves in k, with n << (char(k)) or char(k) = 0. Then either A) there are at most O(n) points in k hit by at least two curves, or B) at least Ω(n) curves from L must lie on a bounded-degree surface, and many of ...
متن کاملAbelian Points on Algebraic Curves
We study the question of whether algebraic curves of a given genus g defined over a field K must have points rational over the maximal abelian extension K of K. We give: (i) an explicit family of diagonal plane cubic curves without Q-points, (ii) for every number field K, a genus one curve C/Q with no K -points, and (iii) for every g ≥ 4 an algebraic curve C/Q of genus g with no Q-points. In an...
متن کاملAbelian Points on Algebraic Varieties
We attempt to determine which classes of algebraic varieties over Q must have points in some abelian extension of Q. We give: (i) for every odd d > 1, an explicit family of degree d, dimension d − 2 diagonal hypersurfaces without Qab-points, (ii) for every number field K, a genus one curve C/Q with no K ab-points, and (iii) for every g ≥ 4 an algebraic curve C/Q of genus g with no Qab-points. I...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2006
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2005.10.016