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Local and global heights on weighted projective varieties

Sajad Salami, Tanush Shaska

I-AIMS paper 2022-1 · Published in Houston J. Math. 49 (2023), no. 3, 603–636 · 2023

We investigate local and global weighted heights à la Weil for weighted projective spaces via Cartier and Weil divisors and extend the definition of weighted heights on weighted projective spaces 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.

MSC classes: Primary 11G50; Secondary 14G40

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