English

Integral points of bounded height on a certain toric variety

Number Theory 2025-05-19 v2 Algebraic Geometry

Abstract

We determine an asymptotic formula for the number of integral points of bounded height on a certain toric variety, which is incompatible with part of a preprint by Chambert-Loir and Tschinkel. We provide an alternative interpretation of the asymptotic formula we get. To do so, we construct an analogue of Peyre's constant α\alpha and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties.

Keywords

Cite

@article{arxiv.2202.10909,
  title  = {Integral points of bounded height on a certain toric variety},
  author = {Florian Wilsch},
  journal= {arXiv preprint arXiv:2202.10909},
  year   = {2025}
}

Comments

26 pages, 4 figures; author accepted version, appeared in Trans. Amer. Math. Soc. Ser. B