Details
| Original language | English |
|---|---|
| Pages (from-to) | 567-599 |
| Number of pages | 33 |
| Journal | Transactions of the American Mathematical Society Series B |
| Volume | 11 |
| Publication status | Published - 26 Feb 2024 |
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 and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties.
Keywords
- Integral point, Manin’s conjecture, toric variety
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics (miscellaneous)
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In: Transactions of the American Mathematical Society Series B, Vol. 11, 26.02.2024, p. 567-599.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Integral points of bounded height on a certain toric variety
AU - Wilsch, Florian
N1 - Publisher Copyright: © 2024, American Mathematical Society. All rights reserved.
PY - 2024/2/26
Y1 - 2024/2/26
N2 - 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 and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties.
AB - 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 and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties.
KW - Integral point
KW - Manin’s conjecture
KW - toric variety
UR - http://www.scopus.com/inward/record.url?scp=85201175215&partnerID=8YFLogxK
U2 - 10.1090/btran/166
DO - 10.1090/btran/166
M3 - Article
AN - SCOPUS:85201175215
VL - 11
SP - 567
EP - 599
JO - Transactions of the American Mathematical Society Series B
JF - Transactions of the American Mathematical Society Series B
SN - 2330-0000
ER -