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arXiv · 2204.01624

Local and Global Heights on Weighted Projective Varieties

Sajad Salami·Tony Shaska
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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 $M$-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.

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Sajad Salami, Tony Shaska. 2022-04-04. Local and Global Heights on Weighted Projective Varieties. https://arxiv.org/abs/2204.01624

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