Thin sets in weighted projective stacks

TL;DR

This paper establishes an upper bound on rational points in weighted projective stacks within thin subsets and applies this to show that almost all hyperelliptic curves lack certain level structures.

Contribution

It introduces bounds for rational points in weighted projective stacks and demonstrates a generic non-existence of specific level structures on hyperelliptic curves.

Findings

Upper bound for rational points in weighted projective stacks

Almost all hyperelliptic curves lack a prescribed level structure

Thin sets contain negligible rational points in this context

Abstract

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.