منابع مشابه
Counting Rational Points on K3 Surfaces
For any algebraic variety X defined over a number field K, and height functionHD onX corresponding to an ample divisorD, one can define the counting functionNX,D(B) = #{P ∈ X(K) | HD(P ) ≤ B}. In this paper, we calculate the counting function for hyperelliptic K3 surfaces X which admit a generically two-to-one cover of P1 × P1 branched over a singular curve. In particular, we effectively constr...
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We provide a real analog of the Yau-Zaslow formula counting rational curves on K3 surfaces. ”But man is a fickle and disreputable creature and perhaps, like a chess-player, is interested in the process of attaining his goal rather than the goal itself.” Fyodor Dostoyevsky, Notes from the Underground.
متن کاملRational double points on supersingular K3 surfaces
We investigate configurations of rational double points with the total Milnor number 21 on supersingular K3 surfaces. The complete list of possible configurations is given. As an application, we also give the complete list of extremal (quasi-)elliptic fibrations on supersingular K3 surfaces.
متن کاملRational 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...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2000
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2533