Rational and integral points on Markoff-type K3 surfaces
Abstract
Following recent works by E. Fuchs et al. and by the author, we study rational and integral points on Markoff-type K3 (MK3) surfaces, i.e., Wehler K3 surfaces of Markoff type. In particular, we construct a family of MK3 surfaces which have a Zariski dense set of rational points but fail the integral Hasse principle due to the Brauer-Manin obstruction and provide some counting results for this family. We also give some remarks on Brauer groups, Picard groups, and failure of strong approximation on MK3 surfaces.
Cite
@article{arxiv.2504.10992,
title = {Rational and integral points on Markoff-type K3 surfaces},
author = {Quang-Duc Dao},
journal= {arXiv preprint arXiv:2504.10992},
year = {2025}
}
Comments
28 pages; comments are welcome; added an assumption to Proposition 3.2 and rewrote the statement, added some details to the proof, the result remains the same; revised some assumptions for technical reasons, the main results stay the same; updated and added references. arXiv admin note: substantial text overlap with arXiv:2302.11515