Brilliant Points of Curves and Surfaces
نویسندگان
چکیده
منابع مشابه
Rational Curves and Points on K3 Surfaces
— We study the distribution of algebraic points on K3 surfaces.
متن کاملK3 Surfaces, Rational Curves, and Rational Points
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. Mathematics Subj...
متن کاملK3 Surfaces, Rational Curves, and Rational Points
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. Mathematics Subj...
متن کاملThe Density of Rational Points on Curves and Surfaces
Let n ≥ 3 be an integer and let F (x) = F (x1, . . . , xn) ∈ Z[x1, . . . , xn] be an absolutely irreducible form of degree d, producing a hypersurface of dimension n − 2 in Pn−1. This paper is primarily concerned with the number of rational points on this hypersurface, of height at most B, say. In order to describe such points we choose representatives x = (x1, . . . , xn) ∈ Z with the xi not a...
متن کاملNodal Curves and Postulation of Generic Fat Points on Surfaces
Let X be a smooth projective surface. Here we study the postulation of a general union Z of fat points of X, when most of the connected components of Z have multiplicity 2. This problem is related to the existence of ”good” families of curves on X, with prescribed singularities, most of them being nodes, and to the cohomology of suitable line bundles on blowing ups of X. More precise statements...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1908
ISSN: 0002-9947
DOI: 10.2307/1988604