Height on GIT quotients and Kempf-Ness theory
Algebraic Geometry
2014-11-26 v1 Number Theory
Abstract
In this paper we study heights on quotient varieties in the sense of Geometric Invariant Theory (GIT). We generalise a construction of Burnol and we generalise diverse lower bounds of the height of semi-stable points due to Bost, Zhang, Gasbarri and Chen. In order to prove Burnol's formula for the height on the quotient we develop a Kempf-Ness theory in the setting of Berkovich analytic spaces, completing the former work of Burnol.
Keywords
Cite
@article{arxiv.1411.6786,
title = {Height on GIT quotients and Kempf-Ness theory},
author = {Marco Maculan},
journal= {arXiv preprint arXiv:1411.6786},
year = {2014}
}