Thin sets in weighted projective stacks

We prove an upper bound for the number of rational points of bounded height in a weighted projective stack which lie in a given thin subset. As a consequence, we show that $100%$ of hyperelliptic curves do not admit a prescribed on-trivial level structure.

💡 Research Summary

The paper “Thin sets in weighted projective stacks” studies the distribution of rational points of bounded height on weighted projective stacks and applies the results to level structures on hyperelliptic curves. The authors first recall the classical notion of thin sets introduced by Serre for varieties, then extend it to Deligne–Mumford stacks following the work of Darda–Yasuda. In this framework a thin subset of a stack is a finite union of images of non‑birational, representable, generically finite morphisms (the stack analogue of Type I and Type II thin sets).

A weighted projective stack is defined as the quotient stack
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