The Manin–Peyre conjecture for smooth spherical Fano threefolds

verfasst von

Valentin Blomer, Jörg Brüdern, Ulrich Derenthal, Giuliano Gagliardi

Abstract

The Manin–Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N. Together with the previously solved case T and the toric cases, this covers all types of smooth spherical Fano threefolds. The case N features a number of structural novelties; most notably, one may lose regularity of the ambient toric variety, the height conditions may contain fractional exponents, and it may be necessary to exclude a thin subset with exceptionally many rational points from the count, as otherwise Manin’s conjecture in its original form would turn out to be incorrect.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Rheinische Friedrich-Wilhelms-Universität Bonn
Georg-August-Universität Göttingen
Institute for Advanced Studies

Typ

Artikel

Journal

Selecta Mathematica, New Series

Band

30

ISSN

1022-1824

Publikationsdatum

09.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Allgemeine Mathematik, Allgemeine Physik und Astronomie

Elektronische Version(en)

https://doi.org/10.1007/s00029-024-00952-4 (Zugang: Offen)
https://doi.org/10.48550/arXiv.2203.14841 (Zugang: Offen)