Counting Rational Points on K3 Surfaces
| dc.creator | McKinnon, David | |
| dc.date | 1999-03-02 | |
| dc.date | 1999-03-04 | |
| dc.date.accessioned | 2026-07-07T05:28:11Z | |
| dc.date.available | 2026-07-07T05:28:11Z | |
| dc.description | For any algebraic variety $V$ defined over a number field $k$, and ample height function $H$ on $V$, one can define the counting function $N_V(B) = #{P\in V(k) \mid H(P)\leq B}$. In this paper, we calculate the counting function for Kummer surfaces $V$ whose associated abelian surface is the product of elliptic curves. In particular, we effectively construct a finite union $C = \cup C_i$ of curves $C_i$ on $V$ such that $N_{V-C}(B)\ll N_C(B)$; that is, $C$ is an accumulating subset of $V$. In the terminology of Batyrev and Manin, this amounts to proving that $C$ is the first layer of the arithmetic stratification of $V$. | |
| dc.description | LaTeX, 9 pages, no figures. Typo corrected, acknowledgements added, a few minor clarifications | |
| dc.identifier | https://arxiv.org/abs/math/9903013 | |
| dc.identifier | http://arxiv.org/abs/math/9903013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78165 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.title | Counting Rational Points on K3 Surfaces | |
| dc.type | text |