Weighted Heights and GIT Heights
Algebraic Geometry
2025-12-09 v2 Number Theory
Abstract
We investigate the relationship between Geometric Invariant Theory (GIT) heights and weighted heights, with a focus on their interaction in weighted projective spaces and their application to binary forms. Building on the weighted height framework developed in previous papers, we relate it to Zhang's GIT height via the Veronese map. For a semistable cycle, we show that the GIT height decomposes into the logarithmic weighted height plus an Archimedean correction from the Chow metric.
Keywords
Cite
@article{arxiv.2503.17068,
title = {Weighted Heights and GIT Heights},
author = {Elira Shaska and Tony Shaska},
journal= {arXiv preprint arXiv:2503.17068},
year = {2025}
}