On K-stability, height bounds and the Manin-Peyre conjecture
R. Berman. (2023)cite arxiv:2305.07272Comment: 30 pages.
Abstract
This note discusses some intriguing connections between height bounds on
complex K-semistable Fano varieties X and Peyre's conjectural formula for the
density of rational points on X. Relations to an upper bound for the smallest
rational point, proposed by Elsenhans-Jahnel, are also explored. These
relations suggest an analog of the height inequalities, adapted to the real
points, which is established for the real projective line and related to
Kähler-Einstein metrics.
Description
On K-stability, height bounds and the Manin-Peyre conjecture
%0 Generic
%1 berman2023kstability
%A Berman, Robert J.
%D 2023
%K Manin-Peyre conjecture k-stable
%T On K-stability, height bounds and the Manin-Peyre conjecture
%U http://arxiv.org/abs/2305.07272
%X This note discusses some intriguing connections between height bounds on
complex K-semistable Fano varieties X and Peyre's conjectural formula for the
density of rational points on X. Relations to an upper bound for the smallest
rational point, proposed by Elsenhans-Jahnel, are also explored. These
relations suggest an analog of the height inequalities, adapted to the real
points, which is established for the real projective line and related to
Kähler-Einstein metrics.
@misc{berman2023kstability,
abstract = {This note discusses some intriguing connections between height bounds on
complex K-semistable Fano varieties X and Peyre's conjectural formula for the
density of rational points on X. Relations to an upper bound for the smallest
rational point, proposed by Elsenhans-Jahnel, are also explored. These
relations suggest an analog of the height inequalities, adapted to the real
points, which is established for the real projective line and related to
K\"ahler-Einstein metrics.},
added-at = {2023-06-16T02:10:35.000+0200},
author = {Berman, Robert J.},
biburl = {https://www.bibsonomy.org/bibtex/2d2db4d87763d12fb75953cb3d2ea5ee6/soulcraw},
description = {On K-stability, height bounds and the Manin-Peyre conjecture},
interhash = {9c5b5881b7ea4433d39f708d2e874591},
intrahash = {d2db4d87763d12fb75953cb3d2ea5ee6},
keywords = {Manin-Peyre conjecture k-stable},
note = {cite arxiv:2305.07272Comment: 30 pages},
timestamp = {2023-06-21T04:36:22.000+0200},
title = {On K-stability, height bounds and the Manin-Peyre conjecture},
url = {http://arxiv.org/abs/2305.07272},
year = 2023
}