The Manin conjecture for toric stacks

Ratko Darda, Takehiko Yasuda

Published 2023-11-03Version 1

Split toric stacks over a number field $F$ are natural generalization of split toric varieties over $F$. Notable examples are weighted projective stacks. In our previous work, we defined heights on Deligne-Mumford stacks using so-called raised line bundles and made predictions on asymptotic formulas of the number of rational points of bounded height. In this paper, we prove that the number of rational points of any split toric stack of bounded height with respect to the anti-canonical raised line bundle satisfies one of our predictions, the Manin conjecture for Deligne-Mumford stacks.