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arXiv · 1411.6786

Height on GIT quotients and Kempf-Ness theory

Marco Maculan
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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.

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Marco Maculan. 2014-11-25. Height on GIT quotients and Kempf-Ness theory. https://arxiv.org/abs/1411.6786

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