K3 surfaces, rational curves, and rational points

Details K3 surfaces, rational curves, and rational points K3 surfaces, rational curves, and rational points

2007-09-05

arxiv.org/abs/0709.0663v3

Mathematics

Algebraic Geometry

10 pages, no figures. An explicit construction of an algebraic point lying on no smooth rational curves has been added to the

Scientific paper

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. We apply our results to construct an explicit algebraic point on a $K3$ surface that does not lie on any smooth rational curves.

Affiliated with

Also associated with

No associations

Rating

K3 surfaces, rational curves, and rational points does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with K3 surfaces, rational curves, and rational points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and K3 surfaces, rational curves, and rational points will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-470747