| |
|
Kenneth Ascher and Ariyan Javanpeykar
Bounding heights uniformly in families of hyperbolic varieties view print
|
|
| Published: |
December 11, 2017 |
| Keywords: |
Vojta's Conjecture, hyperbolicity, heights, general type, rational points, moduli spaces |
| Subject: |
14G05, 11G50 |
|
|
Abstract
We show, assuming Vojta's height conjecture, the height of a rational point on an algebraically hyperbolic variety can be bounded "uniformly'' in families. This generalizes a result of Su-Ion Ih for curves of genus at least two to higher-dimensional varieties. As an application, we show that, assuming Vojta's height conjecture, the height of a rational point on a curve of general type is uniformly bounded. Finally, we prove a similar result for smooth hyperbolic surfaces with c12 > c2.
|
|
| Acknowledgements
K.A. was supported in part by funds from NSF grant DMS-1162367 and an NSF Postdoctoral Fellowship. A.J. gratefully acknowledges support from SFB/Transregio 45.
|
|
| Author information
Kenneth Ascher:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02138, USA
kascher@mit.edu
Ariyan Javanpeykar:
Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55099 Mainz, Germany
peykar@uni-mainz.de
|
|
