Local and global heights on weighted projective varieties

Authors

• 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

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 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.