Publication details
The Manin–Peyre conjecture for smooth spherical Fano threefolds
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.
Details
- 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 )
