# Integral points of bounded height on a certain toric variety

Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv, 2202.10909.

Preprint | Submitted | English
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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 $\alpha$ and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties.
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Date Published
2022-02-22
Journal Title
arXiv
Acknowledgement
Part of this work was conducted as a guest at the Institut de Mathématiques de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD. During this time, I had interesting and fruitful discussions on the interpretation of the result for the toric variety discussed in Section 3 with Antoine Chambert-Loir. I wish to thank him for these opportunities and for his useful remarks on earlier versions of this article. This work was partly funded by FWF grant P 32428-N35.
Article Number
2202.10909
Page
25
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### Cite this

Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv.
Wilsch, F. A. (n.d.). Integral points of bounded height on a certain toric variety. arXiv.
Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain Toric Variety.” ArXiv, n.d.
F. A. Wilsch, “Integral points of bounded height on a certain toric variety,” arXiv. .
Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv, 2202.10909.
Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain Toric Variety.” ArXiv, 2202.10909.
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arXiv 2202.10909