The Manin-Peyre conjecture for smooth spherical Fano varieties of semisimple rank one
Valentin Blomer, J\"org Br\"udern, Ulrich Derenthal, Giuliano, Gagliardi
TL;DR
This paper proves the Manin-Peyre conjecture for a class of smooth spherical Fano varieties of semisimple rank one, including all smooth spherical Fano threefolds of type T and some higher-dimensional cases.
Contribution
It establishes the conjecture for a broad class of smooth spherical Fano varieties of semisimple rank one, expanding known cases.
Findings
Manin-Peyre conjecture verified for these varieties
Includes all smooth spherical Fano threefolds of type T
Extends to some higher-dimensional cases
Abstract
The Manin-Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as well as some higher-dimensional smooth spherical Fano varieties.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds