The Manin–Peyre conjecture for smooth spherical Fano threefolds

authored by

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of Bonn
University of Göttingen
Institute for Advanced Studies

Type

Article

Journal

Selecta Mathematica, New Series

Volume

30

ISSN

1022-1824

Publication date

09.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics, General Physics and Astronomy

Electronic version(s)

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