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.
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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
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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
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Cite this
Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv. doi:10.48550/arXiv.2202.10909
Wilsch, F. A. (n.d.). Integral points of bounded height on a certain toric variety. arXiv. https://doi.org/10.48550/arXiv.2202.10909
Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain Toric Variety.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2202.10909.
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, doi:10.48550/arXiv.2202.10909.
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