Rational Points on Generic Marked Hypersurfaces

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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  • Qixiao Ma

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OriginalspracheEnglisch
Aufsatznummer49
FachzeitschriftMathematische Zeitschrift
Jahrgang306
Ausgabenummer3
PublikationsstatusVeröffentlicht - 14 Feb. 2024

Abstract

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 \(\mathbb{P}^{n+1}\).

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Rational Points on Generic Marked Hypersurfaces. / Ma, Qixiao.
in: Mathematische Zeitschrift, Jahrgang 306, Nr. 3, 49, 14.02.2024.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Ma Q. Rational Points on Generic Marked Hypersurfaces. Mathematische Zeitschrift. 2024 Feb 14;306(3):49. doi: 10.48550/arXiv.2309.12208, 10.1007/s00209-023-03423-2
Ma, Qixiao. / Rational Points on Generic Marked Hypersurfaces. in: Mathematische Zeitschrift. 2024 ; Jahrgang 306, Nr. 3.
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