Sajad Salami, Institute of Mathematics and Statistics and State University of Rio de Janeiro, Rio de Janeiro, Brazil
Tony Shaska, Department of Mathematics and Statistics, Oakland University, Rochester Hills, MI
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 Beshaj, Gutierrez, Shaska (2020) 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.
