Details
| Original language | English |
|---|---|
| Article number | 49 |
| Journal | Mathematische Zeitschrift |
| Volume | 306 |
| Issue number | 3 |
| Publication status | Published - 14 Feb 2024 |
Abstract
Keywords
- math.AG, math.GT, 14G05, 14G27, 14J70, Primary: 14G05 14J70, Rational points, Generic hypersurfaces, Franchetta conjecture, Secondary: 14G27 14M20
ASJC Scopus subject areas
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Mathematische Zeitschrift, Vol. 306, No. 3, 49, 14.02.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Rational Points on Generic Marked Hypersurfaces
AU - Ma, Qixiao
PY - 2024/2/14
Y1 - 2024/2/14
N2 - Over fields of characteristic zero, we show that for \(n=1,d\geq4\) or \(n=2,d\geq5\) or \(n\geq3, d\geq 2n\), the generic \(m\)-marked degree-\(d\) hypersurface in \(\mathbb{P}^{n+1}\) admits the \(m\) marked points as all the rational points. Over arbitrary fields, we show that for \(n=1,d\geq4\) or \(n\geq2, d\geq 2n+3\), the identiy map is the only rational self-map of the generic degree-\(d\) hypersurface in \(\mathbb{P}^{n+1}\).
AB - Over fields of characteristic zero, we show that for \(n=1,d\geq4\) or \(n=2,d\geq5\) or \(n\geq3, d\geq 2n\), the generic \(m\)-marked degree-\(d\) hypersurface in \(\mathbb{P}^{n+1}\) admits the \(m\) marked points as all the rational points. Over arbitrary fields, we show that for \(n=1,d\geq4\) or \(n\geq2, d\geq 2n+3\), the identiy map is the only rational self-map of the generic degree-\(d\) hypersurface in \(\mathbb{P}^{n+1}\).
KW - math.AG
KW - math.GT
KW - 14G05, 14G27, 14J70
KW - Primary: 14G05 14J70
KW - Rational points
KW - Generic hypersurfaces
KW - Franchetta conjecture
KW - Secondary: 14G27 14M20
UR - http://www.scopus.com/inward/record.url?scp=85185309683&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2309.12208
DO - 10.48550/arXiv.2309.12208
M3 - Article
VL - 306
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3
M1 - 49
ER -