%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 }