Local and Global Heights on Weighted Projective Varieties
Abstract
We investigate local and global weighted heights a-la Weil for weighted projective spaces via Cartier and Weil divisors and extend the definition of weighted heights on weighted projective spaces from arXiv:1902.06563 to weighted varieties and closed subvarieties. We prove that any line bundle on a weighted variety admits a locally bounded weighted -metric. Using this fact, we define local and global weighted heights for weighted varieties in weighted projective spaces and their closed subschemes and show their fundamental properties.
Cite
@article{arxiv.2204.01624,
title = {Local and Global Heights on Weighted Projective Varieties},
author = {Sajad Salami and Tony Shaska},
journal= {arXiv preprint arXiv:2204.01624},
year = {2023}
}
Comments
The paper was posted earlier in a longer version and called "Local and global heights on weighted projective varieties and Vojta's conjecture". After the referees suggestions it was split into two papers. This is the first one of the two, which in cludded a modified proof for Proposition 4