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

Type

Preprint

Publication date

28.03.2022

Publication status

E-pub ahead of print

Electronic version(s)

https://doi.org/10.48550/arXiv.2203.14841 (Access: Open)