Details
| Original language | English |
|---|---|
| Pages (from-to) | 39-82 |
| Number of pages | 44 |
| Journal | Advances in mathematics |
| Volume | 337 |
| Early online date | 28 Aug 2018 |
| Publication status | Published - 15 Oct 2018 |
Abstract
We prove Manin's conjecture on the asymptotic behavior of the number of rational points of bounded anticanonical height for a spherical threefold with canonical singularities and two infinite families of spherical threefolds with log terminal singularities. Moreover, we show that one of these families does not satisfy a conjecture of Batyrev and Tschinkel on the leading constant in the asymptotic formula. Our proofs are based on the universal torsor method, using Brion's description of Cox rings of spherical varieties.
Keywords
- Fano threefolds, Manin's conjecture, Rational points, Spherical varieties
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Advances in mathematics, Vol. 337, 15.10.2018, p. 39-82.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Manin's conjecture for certain spherical threefolds
AU - Derenthal, Ulrich
AU - Gagliardi, Giuliano
PY - 2018/10/15
Y1 - 2018/10/15
N2 - We prove Manin's conjecture on the asymptotic behavior of the number of rational points of bounded anticanonical height for a spherical threefold with canonical singularities and two infinite families of spherical threefolds with log terminal singularities. Moreover, we show that one of these families does not satisfy a conjecture of Batyrev and Tschinkel on the leading constant in the asymptotic formula. Our proofs are based on the universal torsor method, using Brion's description of Cox rings of spherical varieties.
AB - We prove Manin's conjecture on the asymptotic behavior of the number of rational points of bounded anticanonical height for a spherical threefold with canonical singularities and two infinite families of spherical threefolds with log terminal singularities. Moreover, we show that one of these families does not satisfy a conjecture of Batyrev and Tschinkel on the leading constant in the asymptotic formula. Our proofs are based on the universal torsor method, using Brion's description of Cox rings of spherical varieties.
KW - Fano threefolds
KW - Manin's conjecture
KW - Rational points
KW - Spherical varieties
UR - http://www.scopus.com/inward/record.url?scp=85052339075&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1611.04754
DO - 10.48550/arXiv.1611.04754
M3 - Article
AN - SCOPUS:85052339075
VL - 337
SP - 39
EP - 82
JO - Advances in mathematics
JF - Advances in mathematics
SN - 0001-8708
ER -