منابع مشابه
Secant Varieties and Successive Minima
Let X be a semi-stable arithmetic surface over the spectrum S of the ring of integers in a number field K. We assume that the generic fiber XK is geometrically irreducible and has positive genus. Consider a line bundle L on X , which is non-negative on every vertical fiber and equipped with an admissible metric (in the sense of Arakelov [A]) of positive curvature. In [S] we have shown that any ...
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In this note we present inequalities relating the successive minima of a o-symmetric convex body and the successive inner and outer radii of the body. These inequalities build a bridge between known inequalities involving only either the successive minima or the successive radii.
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The goal of this talk is to introduce secant varieies and show connections of secant varieties of Veronese variety to the Waring problem. 1 Secant varieties Let X ⊂ P be a variety over k, where k is algebraically closed field of characteristic 0 (or just assume k = C). Definition 1.1. For s ≥ 1 the s-th higher secant variety of X is
متن کاملSecant Varieties of Toric Varieties
If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...
متن کاملLinear projections and successive minima
In arithmetic geometry, cohomology groups are not vector spaces as in classical algebraic geometry but rather euclidean lattices. As a consequence, to understand these groups we need to evaluate not only their rank, but also their successive minima, which are fundamental invariants in the geometry of numbers. The goal of this article is to perform this task for line bundles on projective curves...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2004
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-03-00351-5